Analysis and Synthesis of Singular Systems with Time-Delays

Wu, Zheng‐Guang; Su, Hongye; Shi, Peng

doi:10.1007/978-3-642-37497-5

Cited by 53 publications

(26 citation statements)

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“…Without loss of generality, as noted in [24], in this section we assume that Q ≤ 0 and denoted that −Q =Q TQ for someQ. In all cases, the inequality should hold for ∀u(t), ∀ > 0 and the corresponding y(t).…”

Section: Definition 92mentioning

confidence: 99%

Dissipativity and Invariant Sets for Neural Networks with Delay

Wang

Liu

Zheng

2015

Qualitative Analysis and Control of Complex Neural Networks With Delays

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Energy dissipation is a fundamental concept in dynamical systems. Passivity and dissipativity characterize the "energy" consumption of a dynamical system and form a powerful tool in many real applications. Passivity is closely related to stability and exhibits a compositional property for parallel and feedback interconnections. Passivity-based control is especially useful in the analysis of complex coupled systems. In Chap. 8, passivity problem is studied for a kind of neural networks with delays. Dissipativity and invariant sets are also the qualitative characteristics of a dynamical system. Such qualitative characteristics as passivity, dissipativity, and invariant sets are extensions and upgrades of the stability property, which can characterize the dynamics of dynamical systems more general. Based on such analysis, in this chapter some sufficient conditions for dissipativity and invariant sets have been established for a kind of RNNs with delay. The contents in this chapter are some extensions of the stability results of previous chapters. Delay-Dependent Dissipativity Conditionsfor Delayed RNNs IntroductionSince the study of dissipative systems was initiated by Willems [1], and further addressed by Hill and Moylan [2], there has been a steady increase in the interest of dissipative systems in the past several decades. The reasons are as follows:(1) The dissipative theory gives a framework for the design and analysis of control systems using an input-output description based on energy-related considerations [3,4]. (2) The dissipative theory serves as a powerful or even indispensable tool in characterizing important system behaviors, such as stability and passivity, and has close connections with passivity theorem, bounded real lemma, Kalman-Yakubovich To name a few, by using a linear matrix inequality (LMI) approach, the problem of quadratic dissipative control for linear systems with or without uncertainty was studied in [6], where some necessary and sufficient conditions were presented for synthesis of feedback controllers to ensure the dissipativity of the resulting closed-loop system. In [7], by proposing multiple storage functions and multiple supply rates, a framework of dissipativity theory for switched systems was established. More recently, some dissipativity conditions were presented in [8] for singular systems. When stochastic noise was taken into consideration in studying dissipative systems, the problems of sliding mode control were tackled in [9]. In [10], the robust reliable dissipative filtering problem has been investigated for uncertain discrete-time singular system with interval time-varying delays and sensor failures. The problem of static output-feedback dissipative control has been studied for linear continuous-time system based on an augmented system approach in [11]. A necessary and sufficient condition for the existence of a desired controller has been given, and a corresponding iterative algorithm has also been developed to solve the condition.On the other hand, as a special class of...

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Section: Definition 92mentioning

confidence: 99%

Dissipativity and Invariant Sets for Neural Networks with Delay

Wang

Liu

Zheng

2015

Qualitative Analysis and Control of Complex Neural Networks With Delays

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“…The notation y; Su h i F represents R F 0 y T ðtÞSuðtÞdt, and the other symbols are similarly defined. Without loss of generality, as noted in [6,23], we assume that Q 6 0 and denoted that ÀQ ¼Q TQ for someQ . Before proceeding further, we first introduce the following definition and lemma for DNN ðRÞ, which will be important for the derivations of the main results.…”

Section: Daðtþ Dbðtþ Dcðtþmentioning

confidence: 99%

“…In [35], by proposing multiple storage functions and multiple supply rates, a framework of dissipativity theory for switched systems was established. More recently, some dissipativity conditions were presented in [6,23] for singular systems. When stochastic noise was taken into consideration in studying dissipative systems, the problems fuzzy control and sliding mode control were tackled in [20,21], respectively.…”

Section: Introductionmentioning

confidence: 99%

Delay-dependent robust dissipativity conditions for delayed neural networks with random uncertainties

Wang

Park

Shen

2013

Applied Mathematics and Computation

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“…When descriptor systems are subjected to stochastic disturbance in their structures, it is reasonable to cast the model into descriptor Markovian jump systems. Recently, a great deal of attention has been devoted to descriptor Markovian jump systems, to name a few, stability and stabilization (e.g., [25][26][27][28][29][30][31]), guaranteed cost control and H ∞ control (e.g., [22]), observer design (e.g., [32]) and monographs [33,34]. Among these published results, Wang and Zhang [28] studied the robust control problem for a class of uncertain singular stochastic Markovian jump systems via proportional-derivative state feedback controllers, but the derivative-term coefficient is assumed to be normalized which can be transformed into the standard state-space Markovian jump systems.…”

Section: Introductionmentioning

confidence: 99%

Sliding mode control for descriptor Markovian jump systems with mode-dependent derivative-term coefficient

Zhang

Zhai

et al. 2015

Nonlinear Dyn

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This paper concerns sliding mode control problems for a class of descriptor Markovian jump systems with mode-dependent derivative-term coefficient. Firstly, a necessary and sufficient condition, under which such type descriptor Markovian jump systems with mode-dependent derivative-term coefficient are stochastically admissible, is proposed by means of the strictly linear matrix inequality (LMI) technique. Then a novel sliding surface function, in terms of both system states and inputs, is proposed for descriptor Markovian jump systems with mode-dependent derivative-term coefficient and a dynamic sliding mode controller is synthesized, which ensures the reachability of predefined sliding surface in finite time. It is also shown that the stochastic admissibility of the overall closed loop systems can be determined by checking the feasibility of a series of LMIs. Finally, an illustrative example on DC motor is provided to demonstrate the effectiveness of the theoretical results.

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Analysis and Synthesis of Singular Systems with Time-Delays

Cited by 53 publications

References 0 publications

Dissipativity and Invariant Sets for Neural Networks with Delay

Dissipativity and Invariant Sets for Neural Networks with Delay

Delay-dependent robust dissipativity conditions for delayed neural networks with random uncertainties

Sliding mode control for descriptor Markovian jump systems with mode-dependent derivative-term coefficient

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