Journal ArticleDOI
An improved characterization of bounded realness for singular delay systems and its applications
Shengyuan Xu,James Lam,Yun Zou +2 more
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TLDR
In this paper, a delay-dependent bounded real lemma (BRL) for singular systems with a time delay is proposed, which guarantees a singular system to be regular, impulse free and stable while satisfying a prescribed H∞ performance level for any delays smaller than a given upper bound.Abstract:
This paper is concerned with establishing a delay-dependent bounded real lemma (BRL) for singular systems with a time delay. Without resorting to any bounding techniques for some cross terms and model transformation, a new version of BRL for such systems is proposed, which guarantees a singular system to be regular, impulse free and stable while satisfying a prescribed H∞ performance level for any delays smaller than a given upper bound. Based on this, an H∞ state feedback controller is designed via a linear matrix inequality approach. The BRL, stability as well as H∞ results developed in this paper are less conservative than existing ones in the literature, which is demonstrated by providing some numerical examples. Copyright © 2007 John Wiley & Sons, Ltd.read more
Citations
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Journal ArticleDOI
Technical communique: α-Dissipativity analysis of singular time-delay systems
TL;DR: Using the delay partitioning technique, sufficient conditions are established in terms of linear matrix inequalities (LMIs), which guarantees a singular system to be admissible and strictly (Q,S,R)[email protected]
Journal ArticleDOI
H∞ filtering for singular Markovian jump systems with time delay
TL;DR: In this article, a delay-dependent bounded real lemma (BRL) is proposed for a singular Markovian jump system with time delay, based on the BRL and under partial knowledge of the jump rates of the Markov process, both delaydependent and delayindependent sufficient conditions that guarantee the existence of the desired filter are presented.
Journal ArticleDOI
Reachable set estimation for discrete-time linear systems with time delays
TL;DR: The objective is to check whether there exists a bounded set that contains all the system states under zero initial conditions, and an ellipsoid containing the reachable set of the considered system is obtained.
Journal ArticleDOI
A delay-dependent bounded real lemma for singular LPV systems with time-variant delay
Fanbiao Li,Xian Zhang +1 more
TL;DR: In this article, a delay-dependent bounded real lemma (BRL) for singular linear parameter-varying (LPV) systems with time-variant delay is presented.
Journal ArticleDOI
H∞ filtering for singular systems with time‐varying delay
TL;DR: In this paper, delay-range-dependent bounded real lemmas are proposed to guarantee the considered system to be regular, impulse free and exponentially stable while satisfying a prescribed H∞ performance level.
References
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Theory of Functional Differential Equations
TL;DR: In this paper, Liapunov functional for autonomous systems is used to define the saddle point property near equilibrium and periodic orbits for linear systems, which is a generalization of the notion of stable D operators.
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Singular Control Systems
TL;DR: This paper presents a meta-analyses of linear singular systems through system analysis via transfer matrix and feedback control of dynamic compensation for singular systems.
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Delay Effects on Stability: A Robust Control Approach
TL;DR: In this article, Liapunov's second method and LMIs are used for closed-loop stability sets and stability regions in a closed loop with discrete delays and LTIs.
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Introduction to the Theory and Applications of Functional Differential Equations
TL;DR: Theoretical background of functional differential equation models is described in this article, where boundary value problems and Periodic Solutions of Differential Equations (PSE) problems are discussed.
Journal ArticleDOI
A survey of linear singular systems
TL;DR: In this paper, a brief historical review of linear singular systems is presented, followed by a survey of results on their solution and properties, and the frequency domain and time domain approaches are discussed together to sketch an overall picture of the current status of the theory.