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A New Robust Fault Detection Approach to Nonlinear Dynamical Systems
, M.Sc. Thesis Sharif University of Technology ; Sadati, Nasser (Supervisor)
Abstract
In this thesis the problem of optimal robust fault detection has been studied. Optimal Fault Detection Filter (FDF) design, by using a Linear Matrix Inequality (LMI) structure for both linear systems with polytopic uncertainties and nonlinear Lipschitz systems has been considered. In this regard, a novel LMI is introduced which is capable of calculating the maximum lower bound of H− index with great accuracy.Then, based on the parameter-dependent Lyapunov function and the property of having convexity in combination of certain state space equations, the result is extended to polytopic uncertain systems. Afterward the design of an optimal observer-based residual generator, in the sense of...
Robust stability and stabilization of LTI fractional order systems with polytopic and interval uncertainties
, Article 2017 25th Iranian Conference on Electrical Engineering, ICEE 2017, 2 May 2017 through 4 May 2017 ; 2017 , Pages 2253-2258 ; 9781509059638 (ISBN) ; Adelipour, S ; Haeri, M ; Sharif University of Technology
Abstract
This paper proposes a novel representation of uncertain LTI fractional order systems based on the state-space model which contains both interval and polytopic uncertainties. First, a set of linear matrix inequalities, which are sufficient conditions, are presented for analyzing the robust stability of the mentioned systems. Then, some sufficient conditions are obtained for designing a feedback gain matrix to tackle the robust stabilization of the considered systems. Note that the concluded conditions of this paper are valid for fractional systems with a given constant derivative order α in 1 ≤ α < 2 and also, can be employed conservatively for α in 0 < α < 1. Finally, through two numerical...
Robust Stability Analysis of FO-LTI Systems with Interval and Polytopic Uncertainties
, M.Sc. Thesis Sharif University of Technology ; Haeri, Mohammad (Supervisor)
Abstract
In this thesis, a new general state space form for uncertain LTI-fractional order system subjected to interval and polytopic uncertainties is introduced. Robust stability analysis and robust stabilization of presented system are investigated. Fractional derivative order assumed to be a known constant. Sufficient conditions in terms linear matrix inequalities (LMIs) are concluded to check the robust stability of the presented system. Then, these results are extended to derive some sufficient LMI conditions to design a state feedback controller in order to stabilize the mentioned uncertain system robustly. Effectiveness and correctness of presented sufficient conditions and application of...
Reducing conservatism in robust stability analysis of fractional-order-polytopic systems
, Article ISA Transactions ; Volume 119 , 2022 , Pages 106-117 ; 00190578 (ISSN) ; Dehghani, M ; Tavazoei, M. S ; Sharif University of Technology
ISA - Instrumentation, Systems, and Automation Society
2022
Abstract
This paper studies the robust stability of the fractional-order (FO) LTI systems with polytopic uncertainty. Generally, the characteristic polynomial of the system dynamic matrix is not an affine function of the uncertain parameters. Consequently, the robust stability of the uncertain system cannot be evaluated by well-known approaches including LMIs or exposed edges theorem. Here, an over-parameterization technique is developed to convert the main characteristic polynomial into a set of local over-parameterized characteristic polynomials (LOPCPs). It is proved that the robust stability of LOPCPs implies the robust stability of the uncertain system. Then, an algorithm is proposed to explore...
Stabilization of Linear and Nonlinear Differential Inclusions Considering Fractional and Integer order Derivatives
, Ph.D. Dissertation Sharif University of Technology ; Haeri, Mohammad (Supervisor)
Abstract
First, stabilization problem of an integer order-nonlinear differential inclusion (IO-NDI) in the form of tracking problem is investigated and discussed while control inputs are subjected to the sector and dead-zone nonlinearities. Based on two the well-known theorems, the mentioned differential inclusion is modeled by a nonlinear system possessing polytopic uncertainties. For tackling the mentioned problem, sliding mode control (SMC) approach is applied and developed. Second, two issues including stability analysis and stabilization problem of a fractional order-linear differential inclusion (FO-LDI) are studied for both fractional order derivatives and separately. For solving these...
LMI-based sufficient conditions for robust stability and stabilization of LTI-fractional-order systems subjected to interval and polytopic uncertainties
, Article Transactions of the Institute of Measurement and Control ; Volume 37, Issue 10 , 2015 , Pages 1207-1216 ; 01423312 (ISSN) ; Abooee, A ; Haeri, M ; Sharif University of Technology
SAGE Publications Ltd
2015
Abstract
In this paper, by introducing a new general state-space form for uncertain linear time-invariant fractional-order systems subjected to interval and polytopic uncertainties, two problems including robust stability analysis and robust stabilization of the presented systems are investigated. Subsequently, two sufficient conditions in terms of several linear matrix inequalities for the problems mentioned are concluded as two separate theorems. It is assumed that the fractional order α is a known constant belonging to 0 < α < 1. Simulation results of two different numerical examples demonstrate that the provided sufficient conditions are applicable and effective for tackling robust stability and...