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linear-time-invariant-systems
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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) ; 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...
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) ; 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 ; 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...
Oscillations in fractional order LTI systems: Harmonic analysis and further results
, Article Signal Processing ; Volume 93, Issue 5 , 2013 , Pages 1243-1250 ; 01651684 (ISSN) ; 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) ; 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
Stability and Stabilization of Fractional Order Linear Time Invariant Swarm Systems
, Ph.D. Dissertation Sharif University of Technology ; Tavazoei, Mohammad Saleh (Supervisor)
Abstract
In this thesis, stability and stabilization of fractional-order linear time invariant swarm systems are studied. In recent years it has been proved that the exact model of dynamic agents in most of the swarm systems can be modeled more accurate by fractional order differential equations. Stating the motivation of choosing this subject, the achievements of the thesis can be divided into two general parts: Investigating the stability of fractional-order swarm systems and how to stabilize such systems. After introducing the fractional-order systems and fractional-order model of swarm systems in the introduction part, the literature review is presented in Chapter 2. In Chapter 3 the results...
Efficient Transmission and Achievable Rates at Molecular Communication
, Ph.D. Dissertation Sharif University of Technology ; Nasiri-Kenari, Masoumeh (Supervisor) ; Gohari, Amin (Supervisor) ; Mirmohseni, Mahtab (Supervisor)
Abstract
Molecular communication (MC), which has stimulated a great deal of interest in recent years, is a new paradigm for communication among nanoscale biological machines. In MC, molecules are carriers of information and information is encoded into concentration, type or releasing time of molecules. One of the issues in the problem of finding more explicit bounds on the capacity.An approach for bounding mutual information in the low SNR regime using the symmetrized KL divergence is introduced and its applicability to Poisson channels is shown. To the best of our knowledge, the first upper bound on the capacity of Poisson channel with a maximum transmission constraint in the low SNR regime is...
Robust D-stability Analysis of a Class of Interval Fractional Order Systems
,
Ph.D. Dissertation
Sharif University of Technology
;
Fathi Jegarkandi, Mohsen
(Supervisor)
Abstract
Because of advancing fractional calculus and modeling physical phenomena by using fractional calculus more accurately than that by using integer calculus, and also existing uncertainties in models of real world systems, robust stability and performance analysis of fractional order systems are necessary. This thesis deals with the robust -stability analysis of LTI fractional order systems from kind of uncertain typical fractional order systems (UTFOS) and the robust stability analysis of LTI fractional order systems with delays from kind of uncertain retarded type systems (URTS) and uncertain neutral type systems (UNTS) with interval uncertainties. The coefficients of the numerator and the...
Norm-bounded integrity conditions of uncertain multivariable linear time-invariant systems under decentralized control with integral action
, Article Journal of Process Control ; Volume 22, Issue 2 , 2012 , Pages 463-469 ; 09591524 (ISSN) ; Nobakhti, A ; Sharif University of Technology
Abstract
Decentralized controllers with integral action represent a large portion of multivariable controllers currently employed in the process industry. The integrity of these systems with respect to loop failures has been relatively well researched. In particular, important results have been found with respect to the relative gain array (RGA). However, less has been done on the treatment of the integrity of uncertain systems. This paper considers the integrity conditions of uncertain systems with norm-bounded uncertainties, and extends four existing integrity conditions to these uncertain systems. These are: integral stabilizable (IS), integral controllable (IC), integral controllable with...
Robust stability and performance analysis of positive systems using linear programming
, Article 24th Mediterranean Conference on Control and Automation, 21 June 2016 through 24 June 2016 ; 2016 , Pages 100-105 ; 9781467383455 (ISBN) ; Nobakhti, A ; MCA ; Sharif University of Technology
Institute of Electrical and Electronics Engineers Inc
Abstract
This work presents a new necessary and sufficient condition for robust stability and robust performance of positive linear time invariant (LTI) systems with structured uncertainties. It is known that robustness analysis of LTI systems with structured uncertainties requires evaluation of structured singular value (SSV), which is known to be NP-hard. This paper shows that for positive systems, the structured singular value can be estimated efficiently using linear programming. Thus, the robustness analysis of positive systems is simplified to easily verifiable conditions that scale linearly with the dimensions of the system. This property finds great utility in analysis and synthesis of large...
Robust stability analysis of uncertain multiorder fractional systems: young and Jensen inequalities approach
, Article International Journal of Robust and Nonlinear Control ; Volume 28, Issue 4 , March , 2018 , Pages 1127-1144 ; 10498923 (ISSN) ; Tavazoei, M. S ; Sharif University of Technology
John Wiley and Sons Ltd
2018
Abstract
Robust stability analysis of multiorder fractional linear time-invariant systems is studied in this paper. In the present study, first, conservative stability boundaries with respect to the eigenvalues of a dynamic matrix for this kind of systems are found by using Young and Jensen inequalities. Then, considering uncertainty on the dynamic matrix, fractional orders, and fractional derivative coefficients, some sufficient conditions are derived for the stability analysis of uncertain multiorder fractional systems. Numerical examples are presented to confirm the obtained analytical results. Copyright © 2017 John Wiley & Sons, Ltd
A note on the stability of fractional order systems
, Article Mathematics and Computers in Simulation ; Volume 79, Issue 5 , January , 2009 , Pages 1566-1576 ; 03784754 (ISSN) ; Haeri, M ; Sharif University of Technology
2009
Abstract
In this paper, a new approach is suggested to investigate stability in a family of fractional order linear time invariant systems with order between 1 and 2. The proposed method relies on finding a linear ordinary system that possesses the same stability property as the fractional order system. In this way, instead of performing the stability analysis on the fractional order systems, the analysis is converted into the domain of ordinary systems which is well established and well understood. As a useful consequence, we have extended two general tests for robust stability check of ordinary systems to fractional order systems. © 2008 IMACS
On the assignability of LTI systems with arbitrary control structures
, Article International Journal of Control ; 2021 ; 00207179 (ISSN) ; Sharif University of Technology
Taylor and Francis Ltd
2021
Abstract
In this paper, the assignability of linear time-invariant (LTI) systems with respect to arbitrary control structures is addressed. It is well established that the closed-loop spectrum of an LTI system with an arbitrary control structure is confined to the set containing the fixed-modes of the system with respect to that control structure. However, the assignment of the closed-loop spectrum is not merely limited by the existence of fixed-modes in practical scenarios. The pole assignment may require excessive control effort or even become infeasible due to the presence of small perturbations in the system dynamics. To offer more insights in such more realistic scenarios, a continuous measure...
On the assignability of LTI systems with arbitrary control structures
, Article International Journal of Control ; Volume 95, Issue 8 , 2022 , Pages 2098-2111 ; 00207179 (ISSN) ; Sharif University of Technology
Taylor and Francis Ltd
2022
Abstract
In this paper, the assignability of linear time-invariant (LTI) systems with respect to arbitrary control structures is addressed. It is well established that the closed-loop spectrum of an LTI system with an arbitrary control structure is confined to the set containing the fixed-modes of the system with respect to that control structure. However, the assignment of the closed-loop spectrum is not merely limited by the existence of fixed-modes in practical scenarios. The pole assignment may require excessive control effort or even become infeasible due to the presence of small perturbations in the system dynamics. To offer more insights in such more realistic scenarios, a continuous measure...
Stabilization of fractional order systems using a finite number of state feedback laws
, Article Nonlinear Dynamics ; Volume 66, Issue 1-2 , 2011 , Pages 141-152 ; 0924090X (ISSN) ; Sedigh, A. K ; Haeri, M ; Sharif University of Technology
Abstract
In this paper, the stabilization of linear time-invariant systems with fractional derivatives using a limited number of available state feedback gains, none of which is individually capable of system stabilization, is studied. In order to solve this problem in fractional order systems, the linear matrix inequality (LMI) approach has been used for fractional order systems. A shadow integer order system for each fractional order system is defined, which has a behavior similar to the fractional order system only from the stabilization point of view. This facilitates the use of Lyapunov function and convex analysis in systems with fractional order 1
Direct synthesis of fixed-order h∞ controllers
, Article IEEE Transactions on Automatic Control ; Volume 60, Issue 10 , July , 2015 , Pages 2704-2709 ; 00189286 (ISSN) ; Nobakhti, A ; Sharif University of Technology
Institute of Electrical and Electronics Engineers Inc
2015
Abstract
This technical note considers the fixed-order H∞ output feedback control design problem for linear time invariant (LTI)systems. The objective is to design a fixed-order controller with guaranteed stability and closed-loop H∞ performance. This problem is NP-hard due to the non-convex rank constraint which appears in the formulation. We propose an algorithm for non-iterative direct synthesis (NODS) of reduced order robust controllers. NODS entails initial computation of two positive-definite matrices via full-order convex LMI conditions. These are then utilized by appropriate eigenvalue decomposition to directly obtain a suboptimal convex formulation for the fixed-order controller
Robust controllability assessment via semi-definite programming
, Article Systems and Control Letters ; Volume 98 , 2016 , Pages 1-7 ; 01676911 (ISSN) ; Nobakhti, A ; Sharif University of Technology
Elsevier B.V
2016
Abstract
This paper presents a new framework for systematic assessment of the controllability of uncertain linear time-invariant (LTI) systems. The objective is to evaluate controllability of an uncertain system with norm-bounded perturbation over the entire uncertain region. The method is based on a singular-value minimization problem, over the entire complex plane. To solve the problem, first, a necessary and sufficient condition is proposed to avert the difficulties of griding over the complex plane, and to verify the controllability of directed and undirected networks in a single step. Secondly, the results are utilized to formulate the problem as two Lyapunov-based linear matrix inequalities...
Robust decomposition and structured control of an islanded multi-DG microgrid
, Article IEEE Transactions on Smart Grid ; 2018 ; 19493053 (ISSN) ; Nobakhti, A ; Sharif University of Technology
Institute of Electrical and Electronics Engineers Inc
2018
Abstract
This paper presents a new robust control strategy for islanded operation of a microgrid consisting of several distributed generation (DG) units with arbitrary topology. Each DG unit is connected to its local load through a voltage-source converter (VSC), a series RL filter and a step-up transformer. The multi-DG microgrid with arbitrary connectivity graph is modeled as a linear time-invariant (LTI) system subject to a parametric, norm-bounded uncertain block. By utilizing the developed model for multi-DG microgrids, a systematic approach for the design of structured dynamic output feedback control is proposed. A convex optimization problem is developed which yields a low-order dynamic...
Fractional order MIMO controllers for robust performance of airplane longitudinal motion
, Article Aerospace Science and Technology ; Volume 91 , 2019 , Pages 617-626 ; 12709638 (ISSN) ; Fathi Jegarkandi, M ; Sharif University of Technology
Elsevier Masson SAS
2019
Abstract
This paper presents fractional order multi-input multi-output (MIMO) controllers for the robust performance of airplane longitudinal motion. A novel necessary and sufficient criterion is offered by using the value set concept to analyze the robust performance of fractional order MIMO uncertain systems based on the location of the characteristic equation roots. The criterion is applicable to all linear time-invariant systems of commensurate and incommensurate orders with complex coefficients. The obtained results are applied to an uncertain linear model of a business airplane to improve the robust performance of its longitudinal motion by decentralized MIMO output feedback and MIMO state...
Global stabilization of Lotka-Volterra systems with interval uncertainty
, Article IEEE Transactions on Automatic Control ; Volume 64, Issue 3 , 2019 , Pages 1209-1213 ; 00189286 (ISSN) ; Yazdanpanah, M. J ; Tavazoei, M. S ; Sharif University of Technology
Institute of Electrical and Electronics Engineers Inc
2019
Abstract
This paper deals with the stabilization of the feasible equilibrium point of a special class of nonlinear quadratic systems known as Lotka-Volterra (LV) systems, in the presence of interval uncertainty via a fixed linear state feedback (FLSF). It is well known that for a linear time-invariant system with interval uncertainty, stability at the vertices of a polytope implies stability in the interior of the whole polytope. It has been shown that this idea can be extended to examine the stability of LV systems in the presence of interval uncertainty, recently. In fact, it has been proved that in spite of nonlinear nature of the system, stability at a special vertex guarantees stability at all...