On controllability and observability for a class of impulsive systems

Guan, Zhi‐Hong; Qian, Ting; Yu, Xinghuo

doi:10.1016/s0167-6911(02)00204-9

Cited by 75 publications

(55 citation statements)

References 8 publications

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“…The authors of [61] investigated the complete controllability of hybrid impulsive integrodifferential systems. In papers [62,63] the necessary and sufficient conditions for state controllability and observability for a class of linear time-varying impulsive systems were considered. In paper [64], the notion of complete controllability for nonlinear stochastic neutral impulsive systems in finite-dimensional spaces is introduced.…”

Section: Introductionmentioning

confidence: 99%

Banach fixed-point theorem in semilinear controllability problems – a survey

Klamka

Babiarz

Niezabitowski

2016

Bulletin of the Polish Academy of Sciences Technical Sciences

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Abstract. The main aim of this article is to review the existing state of art concerning the complete controllability of semilinear dynamical systems. The study focus on obtaining the sufficient conditions for the complete controllability for various systems using the Banach fixedpoint theorem. We describe the results for stochastic semilinear functional integro-differential system, stochastic partial differential equations with finite delays, semilinear functional equations, a stochastic semilinear system, a impulsive stochastic integro-differential system, semilinear stochastic impulsive systems, an impulsive neutral functional evolution integro-differential system and a nonlinear stochastic neutral impulsive system. Finally, two examples are presented.

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Section: Introductionmentioning

confidence: 99%

Banach fixed-point theorem in semilinear controllability problems – a survey

Klamka

Babiarz

Niezabitowski

2016

Bulletin of the Polish Academy of Sciences Technical Sciences

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“…The related stabilization problems are interesting and challenging. The reason of using impulsive control to stabilize the TSFNNs in our work is that impulsive control can give better performance than continuous control in some practical cases [6,22,28].…”

Section: Introductionmentioning

confidence: 99%

Impulsive stabilization of fuzzy neural networks with time-varying delays

Lou

Cui

2012

Arab. J. Math.

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This paper is concerned with stabilization for a class of Takagi-Sugeno fuzzy neural networks (TSFNNs) with time-varying delays. An impulsive control scheme is employed to stabilize a TSFNN. We firstly establish the model of TSFNNs by using fuzzy sets and fuzzy reasoning and propose the problem of impulsive stabilization for this model. Then, we present several stabilization conditions based on Lyapunov function, inequality techniques and linear matrix inequality approach. Two numerical examples are provided to illustrate the efficiency of impulsive stabilization for TSFNNs by using fixed impulsive interval and variable impulsive intervals, respectively. Mathematics Subject Classification 93C10 · 93D15

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“…Controllability of linear and nonlinear impulsive systems in finite dimensional space has been discussed by many authors ( [13], [14], [22]). Li et al ([16]) and Chang ([9]) extended the results to impulsive functional differential systems in Banach spaces by using compact semigroup and the Schaefer fixed point theorem.…”

Section: Introductionmentioning

confidence: 99%

Controllability of nonlocal impulsive functional integrodifferential evolution systems

Radhakrishnan¹,

Balachandran²

2011

J. Nonlinear Sci. Appl.

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Abstract. In this paper, we establish a set of sufficient conditions for the controllability of nonlocal impulsive functional integrodifferential evolution systems with finite delay. The controllability results are obtained with out assuming the compactness condition on the evolution operator by using the semigroup theory and applying the fixed point approach. An example is provided to illustrate the theory.

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On controllability and observability for a class of impulsive systems

Cited by 75 publications

References 8 publications

Banach fixed-point theorem in semilinear controllability problems – a survey

Banach fixed-point theorem in semilinear controllability problems – a survey

Impulsive stabilization of fuzzy neural networks with time-varying delays

Controllability of nonlocal impulsive functional integrodifferential evolution systems

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