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#### How to extend visibility polygons by mirrors to cover invisible segments

, Article 11th International Conference and Workshops on Algorithms and Computation, WALCOM 2017, 29 March 2017 through 31 March 2017 ; Volume 10167 LNCS , 2017 , Pages 42-53 ; 03029743 (ISSN); 9783319539249 (ISBN) Vaezi, A ; Ghodsi, M ; Sharif University of Technology
Springer Verlag  2017
Abstract
Given a simple polygon P with n vertices, the visibility polygon (V P) of a point q (V P(q)), or a segment (formula present) (V P(pq)) inside P can be computed in linear time. We propose a linear time algorithm to extend V P of a viewer (point or segment), by converting some edges of P into mirrors, such that a given non-visible segment (formula present) can also be seen from the viewer. Various definitions for the visibility of a segment, such as weak, strong, or complete visibility are considered. Our algorithm finds every edge such that, when converted to a mirror, makes (formula present) visible to our viewer. We find out exactly which interval of (formula present) becomes visible, by...

#### Visibility extension via mirror-edges to cover invisible segments

, Article Theoretical Computer Science ; Volume 789 , 2019 , Pages 22-33 ; 03043975 (ISSN) Vaezi, A ; Ghodsi, M ; Sharif University of Technology
Elsevier B.V  2019
Abstract
Given a simple polygon P with n vertices, the visibility polygon (VP) of a point q, or a segment pq‾ inside P can be computed in linear time. We propose a linear time algorithm to extend the VP of a viewer (point or segment), by converting some edges of P into mirrors, such that a given non-visible segment uw‾ can also be seen from the viewer. Various definitions for the visibility of a segment, such as weak, strong, or complete visibility are considered. Our algorithm finds every edge that, when converted to a mirror, makes uw‾ visible to our viewer. We find out exactly which interval of uw‾ becomes visible, by every edge middling as a mirror, all in linear time. In other words, in this...

#### Fractional-order linear time invariant swarm systems: Asymptotic swarm stability and time response analysis

, Article Central European Journal of Physics ; Volume 11, Issue 6 , October , 2013 , Pages 845-854 ; 18951082 (ISSN) Soorki, M. N ; Tavazoei, M. S ; Sharif University of Technology
2013
Abstract
This paper deals with fractional-order linear time invariant swarm systems. Necessary and sufficient conditions for asymptotic swarm stability of these systems are presented. Also, based on a time response analysis the speed of convergence in an asymptotically swarm stable fractional-order linear time invariant swarm system is investigated and compared with that of its integer-order counterpart. Numerical simulation results are presented to show the effectiveness of the paper results

#### Robust stability analysis of distributed-order linear time-invariant systems with uncertain order weight functions and uncertain dynamic matrices

, Article Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME ; Volume 139, Issue 12 , 2017 ; 00220434 (ISSN) Taghavian, H ; Tavazoei, M. S ; Sharif University of Technology
Abstract
Bounded-input bounded-output (BIBO) stability of distributed-order linear time-invariant (LTI) systems with uncertain order weight functions and uncertain dynamic matrices is investigated in this paper. The order weight function in these uncertain systems is assumed to be totally unknown lying between two known positive bounds. First, some properties of stability boundaries of fractional distributed-order systems with respect to location of eigenvalues of dynamic matrix are proved. Then, on the basis of these properties, it is shown that the stability boundary of distributed-order systems with the aforementioned uncertain order weight functions is located in a certain region on the complex...

#### Strong structural controllability of networks under time-invariant and time-varying topological perturbations

, Article IEEE Transactions on Automatic Control ; Volume 66, Issue 3 , 2021 , Pages 1375-1382 ; 00189286 (ISSN) Mousavi, S. S ; Haeri, M ; Mesbahi, M ; Sharif University of Technology
Institute of Electrical and Electronics Engineers Inc  2021
Abstract
This article investigates the robustness of strong structural controllability for linear time-invariant and linear time-varying directed networks with respect to structural perturbations, including edge deletions and additions. In this direction, we introduce a new construct referred to as a perfect graph associated with a network with a given set of control nodes. The tight upper bounds on the number of edges that can be added to, or removed from a network, while ensuring strong structural controllability, are then derived. Moreover, we obtain a characterization of critical edge sets, the maximal sets of edges whose any subset can be respectively added to or removed from a network while...

#### Partial integrity of unstable LTI systems

, Article 24th Mediterranean Conference on Control and Automation, 21 June 2016 through 24 June 2016 ; 2016 , Pages 1302-1306 ; 9781467383455 (ISBN) Eslami, M ; Nobakhti, A ; Babazadeh, M ; MCA ; Sharif University of Technology
Institute of Electrical and Electronics Engineers Inc
Abstract
This paper considers the Integral Stabilizability (IS) and partial integrity of Linear Time Invariant (LTI) systems with an unstable sub-system. The main contribution of the paper is to show that if the unstable sub-system can be stabilized by means of output feedback, then one obtains an integrity condition which is actually equivalent to that of open-loop stable systems, with two additional assumptions. This means the condition may be evaluated solely on the basis of plant information and does not rely on the knowledge of the values of the controller parameters

#### Improved Model Order Reduction of LTI Systems with Using LMIs

, M.Sc. Thesis Sharif University of Technology Karimi Jirandehi, Ardeshir (Author) ; Nobakhti, Amin (Supervisor)
Abstract
Order reduction is a very important issue in Control Theory. A growing need for order reduction models in different fields such as simulation, identification, and design of control system shows this significance. Actually, a high-order system makes a great deal of complexity in designing hardware of control system, debugging, and implementation. Till nowadays, many repetitive as well as nonrepetitive methods with various criteria have been introduced to find low-order models. In this research, order reduction of linear time invariant system models is analyzed. The selected criterion for measuring error between original system and reduced order system is the norm of H1 because it is not only...

#### Electrohydrodynamic Stability of a Cylindrical Jet under an Axial Electric Field

Abstract
Due to the large application of electro-sprays in various industries, the study of the stability of electro-hydrodynamic flows is important. This thesis examines the stability of cylindrical liquid jets in the presence of an axial electric field. The definition of this jet is a simplified model of electrospray, electrospinning. In this model, the stability of a free incompressible cylindrical flow with surface tensile strength, conductivity, polarization, viscosity, and dielectric constant is determined, irrespective of the solubility of the jet and the surrounding fluid (air), in the presence of uniform axial electric field has taken. This will be done by adding the forces generated by the...

#### Oscillations in fractional order LTI systems: Harmonic analysis and further results

, Article Signal Processing ; Volume 93, Issue 5 , 2013 , Pages 1243-1250 ; 01651684 (ISSN) Siami, M ; Tavazoei, M. S ; Sharif University of Technology
2013
Abstract
This paper studies undamped oscillations generated by marginally stable fractional order linear time invariant (LTI) systems. In this study, an analytical approach is proposed to be used for harmonic analysis of such oscillations in marginally stable commensurate order LTI systems. Also, it is shown that the Q-semi norm of the limit sets for a trajectory of these systems can be analytically determined based on the Q-semi norm of the initial condition, where Q is a specific matrix. Moreover, this result is extended to the wider class of rational order systems. Finally, some numerical examples are presented to demonstrate the use of the paper results

#### Analysis of oscillations in fractional order LTI systems

, Article ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2011, Washington, DC, 28 August 2011 through 31 August 2011 ; Volume 3, Issue PARTS A AND B , August , 2011 , Pages 235-240 ; 9780791854808 (ISBN) Siami, M ; Tavazoei, M. S ; Sharif University of Technology
Abstract
This paper is devoted to analysis of undamped oscillations generated by fractional order linear time invariant (LTI) systems. At first, the trajectories of marginally stable commensurate order systems are investigated. It is verified that we can not use the time-independent phase flow concept for this kind of systems. Also, the differences with the integer order case are highlighted. Then, it is shown that we can determine the Q-norm of the limit sets of a trajectory for these systems based on the Q-norm of the initial condition. Some numerical examples are brought to confirm the achievements of the paper

#### Weak visibility counting in simple polygons

, Article Journal of Computational and Applied Mathematics ; Volume 288 , November , 2015 , Pages 215-222 ; 03770427 (ISSN) Nouri Bygi, M ; Daneshpajouh, S ; Alipour, S ; Ghodsi, M ; Sharif University of Technology
Elsevier  2015
Abstract
For a simple polygon P of size n, we define weak visibility counting problem (WVCP) as finding the number of visible segments of P from a query line segment pq. We present different algorithms to compute WVCP in sub-linear time. In our first algorithm, we spend O(n7) time to preprocess the polygon and build a data structure of size O(n6), so that we can optimally answer WVCP in O(logn) time. Then, we reduce the preprocessing costs to O(n4+ε) time and space at the expense of more query time of O(log5n). We also obtain a trade-off between preprocessing and query time costs. Finally, we propose an approximation method to reduce the preprocessing costs to O(n2) time and space and O(n1/2+ε) query...

#### Near linear-time community detection in networks with hardly detectable community structure

, Article Proceedings of the 2015 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining, ASONAM 2015, 25 August 2015 through 28 August 2015 ; 2015 , Pages 65-72 ; 9781450338547 (ISBN) Rezaei, A ; Far, S. M ; Soleymani, M ; Pei, J ; Tang, J ; Silvestri, F ; Sharif University of Technology
Association for Computing Machinery, Inc  2015
Abstract
Identifying communities has always been a fundamental task in analysis of complex networks. Many methods have been devised over the last decade for detection of communities. Amongst them, the label propagation algorithm brings great scalability together with high accuracy. However, it has one major flaw; when the community structure in the network is not clear enough, it will assign every node the same label, thus detecting the whole graph as one giant community. We have addressed this issue by setting a capacity for communities, starting from a small value and gradually increasing it over time. Preliminary results show that not only our extension improves the detection capability of the...

#### Automata based model checking for reo connectors

, Article Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 15 April 2009 through 17 April 2009 ; Volume 5961 LNCS , 2010 , Pages 260-275 ; 03029743 (ISSN) ; 3642116221 (ISBN) Bonsangue, M. M ; Izadi, M ; Sharif University of Technology
Abstract
Reo is a connector language for the exogenous composition and orchestration of components in a software system. An operational semantics of Reo connectors can be given in terms of Büchi automata over a suitable alphabet of records, capturing both synchronization and context dependency requirements. In this paper, we define an action based linear time temporal logic for expressing properties of Reo connectors. Formulas can be synthesized into Büchi automata representing Reo connectors, thus leading to an automata based model checking algorithm. By generalizing standard automata based model checking algorithms for linear time temporal logic, we give an efficient on-the-fly algorithm for the...

#### Constrained swarm stabilization of fractional order linear time invariant swarm systems

, Article IEEE/CAA Journal of Automatica Sinica ; Volume 3, Issue 3 , 2016 , Pages 320-331 ; 23299266 (ISSN) Naderi Soorki, M ; Tavazoei, M. S ; Sharif University of Technology
Institute of Electrical and Electronics Engineers Inc
Abstract
This paper deals with asymptotic swarm stabilization of fractional order linear time invariant swarm systems in the presence of two constraints: the input saturation constraint and the restriction on distance of the agents from final destination which should be less than a desired value. A feedback control law is proposed for asymptotic swarm stabilization of fractional order swarm systems which guarantees satisfying the above-mentioned constraints. Numerical simulation results are given to confirm the efficiency of the proposed control method

#### Robust strong structural controllability of networks with respect to edge additions and deletions

, Article 2017 American Control Conference, ACC 2017, 24 May 2017 through 26 May 2017 ; 2017 , Pages 5007-5012 ; 07431619 (ISSN); 9781509059928 (ISBN) Mousavi, S. S ; Haeri, M ; Mesbahi, M ; American Automatic Control Council (AACC); Eaton; et al.; GE Global Research; Mitsubishi Electric Research Laboratories (MERL); United Technologies Research Center (UTRC) ; Sharif University of Technology
Institute of Electrical and Electronics Engineers Inc  2017
Abstract
This paper investigates the robustness of strong structural controllability for linear time-invariant directed networked systems with respect to structural perturbations, including edge additions and deletions. In this regard, an algorithm is presented that is initiated by endowing each node of a network with a successive set of integers. Using this algorithm, a new notion of perfect graphs associated with a network is introduced, and tight upper bounds on the number of edges that can be added to, or removed from a network, while ensuring strong structural controllability, are derived. Moreover, we obtain a characterization of critical edges with respect to edge additions and deletions;...

#### Stochastic non-stationary model for ground motion simulation based on higher-order crossing of linear time variant systems

, Article Journal of Earthquake Engineering ; Volume 21, Issue 1 , 2017 , Pages 123-150 ; 13632469 (ISSN) Waezi, Z ; Rofooei, F. R ; Sharif University of Technology
Abstract
This article introduces a new time-varying model to generate synthetic non-stationary acceleration records using the modified Kanaii-Tajimi model with time-variant parameters. The proposed method can capture two different dominant frequencies per time which makes it suitable for synthesizing the near-field no-pulse earthquake records. A number of closed-form relationships are developed to describe the frequency dependent time-domain level crossings of the simulated records under white noise excitation. The model parameters are optimized using the crossing and Arias intensity properties of the synthetic and target records. The efficiency of the proposed model is demonstrated using a data base...

#### Fixed-order decoupling of interval plant families

, Article Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME ; Volume 139, Issue 1 , 2017 ; 00220434 (ISSN) Negim, M ; Nobakhti, A ; Sharif University of Technology
American Society of Mechanical Engineers (ASME)  2017
Abstract
A method for the reduction of interactions in linear time invariant (LTI) multivariable uncertain systems is proposed. An H∞-norm metric is proposed for the assessment of interactions in interval uncertain multiple-input multiple-output (MIMO) plants. Based on this, a procedure for the design of fixed-order dynamic decoupling precompensators for MIMO plants with interval uncertainty is outlined which can be solved using efficient solvers such as CVX. The proposed methodology is used to develop a low-order robust multivariable controller for voltage and frequency control of an islanded distributed generation (DG) unit. Copyright © 2017 by ASME

#### Algebraic conditions for stability analysis of linear time-invariant distributed order dynamic systems: a lagrange inversion theorem approach

, Article Asian Journal of Control ; 2018 ; 15618625 (ISSN) Taghavian, H ; Tavazoei, M. S ; Sharif University of Technology
Wiley-Blackwell  2018
Abstract
BIBO stability of linear time-invariant (LTI) distributed order dynamic systems with non-negative weight functions is investigated in this paper by using Lagrange inversion theorem. New sufficient conditions of stability/instability are presented for these systems accordingly. These algebraically simple conditions are relatively tight and their conservatism is adjustable. © 2018 Chinese Automatic Control Society and John Wiley & Sons Australia, Ltd

#### Strong structural controllability of signed networks

, Article 58th IEEE Conference on Decision and Control, CDC 2019, 11 December 2019 through 13 December 2019 ; Volume 2019-December , 2019 , Pages 4557-4562 ; 07431546 (ISSN); 9781728113982 (ISBN) Mousavi, S. S ; Haeri, M ; Mesbahi, M ; Sharif University of Technology
Institute of Electrical and Electronics Engineers Inc  2019
Abstract
In this paper, we discuss the controllability of a family of linear time-invariant (LTI) networks defined on a signed graph. In this direction, we introduce the notion of positive and negative signed zero forcing sets for the controllability analysis of positive and negative eigenvalues of system matrices with the same sign pattern. A sufficient combinatorial condition that ensures the strong structural controllability of signed networks is then proposed. Moreover, an upper bound on the maximum multiplicity of positive and negative eigenvalues associated with a signed graph is provided. © 2019 IEEE

#### Algebraic conditions for stability analysis of linear time-invariant distributed order dynamic systems: a lagrange inversion theorem approach

, Article Asian Journal of Control ; Volume 21, Issue 2 , 2019 , Pages 879-890 ; 15618625 (ISSN) Taghavian, H ; Tavazoei, M. S ; Sharif University of Technology
Wiley-Blackwell  2019
Abstract
BIBO stability of linear time-invariant (LTI) distributed order dynamic systems with non-negative weight functions is investigated in this paper by using Lagrange inversion theorem. New sufficient conditions of stability/instability are presented for these systems accordingly. These algebraically simple conditions are relatively tight and their conservatism is adjustable. © 2018 Chinese Automatic Control Society and John Wiley & Sons Australia, Ltd