Proceedings ArticleDOI
Singularly impulsive or generalized impulsive dynamical systems: Lyapunov and asymptotic stability
N.A. Kablar
- Vol. 1, pp 173-175
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TLDR
In this paper, singularly impulsive or generalized impulsive dynamical systems are defined as the class of hybrid systems, where algebraic equations represent constraints that differential and difference equations need to satisfy.Abstract:
In this paper we present singularly impulsive or generalized impulsive dynamical systems. Dynamics of this system is characterized by the set of differential, difference, and algebraic equations. They represent the class of hybrid systems, where algebraic equations represent constraints that differential and difference equations need to satisfy. Generalized term have as source generalized systems theory where singular system theory can be viewed as generalization of regular system theory. For this class of system we develop Lyapunov and asymptotic stability theorems.read more
Citations
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Proceedings ArticleDOI
Stabilization of Discontinuous Singular Systems with Markovian Switching and saturating inputs
J. Raouf,El-Kébir Boukas +1 more
TL;DR: The design procedure via linear matrix inequality technique (LMI), the complementarity cone approach and the sequential linear programming matrix method (SLPMM) are used to determine simultaneously a state feedback control and an associated domain of safe admissible states for which the regularity, the absence of impulsive behavior and the stochastic stability of the closed-loop systems are guaranteed.
Journal ArticleDOI
Stabilization of Singular Markovian Jump Systems with Discontinuities and Saturating Inputs
J. Raouf,E. K. Boukas +1 more
TL;DR: In this paper, the stability and stabilization of Markov jumping singular systems with discontinuities and saturating inputs is addressed by using linear matrix inequality technique (LMI) and the sequential linear programming matrix method (SLPMM).
Journal ArticleDOI
H-infinity control for switched and impulsive singular systems
TL;DR: In this paper, a new model of dynamical systems is proposed which consists of singular systems with impulsive effects, i.e., switched and impulsive singular systems (SISS), and a sufficient condition for the solvability of the H-infinity control problem for SISSs is given.
Proceedings ArticleDOI
Hybrid Control for a Class of Switched Singular Systems with State Jumps
Yujuan Yin,Jun Zhao +1 more
TL;DR: In this article, a hybrid switching law for switched singular systems with state jumps is designed and a sufficient condition for the system to be asymptotically stable is formulated by solving a set of LMIs.
Proceedings ArticleDOI
Finite time stability of singularly impulsive dynamical systems
TL;DR: Finite-time stability results for nonlinear singularly impulsive dynamical systems by using quasi-Lyapunov function approach are presented and extensive applications can be found in contact problems and in hybrid systems.
References
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Book
Linear Matrix Inequalities in System and Control Theory
TL;DR: In this paper, the authors present a brief history of LMIs in control theory and discuss some of the standard problems involved in LMIs, such as linear matrix inequalities, linear differential inequalities, and matrix problems with analytic solutions.
MonographDOI
Impulsive differential equations
TL;DR: General description of impulsive differential systems linear systems stability of solutions periodic and almost periodic impulsive systems integral sets ofImpulsive systems optimal control in Impulsive systems asymptotic study of oscillations in impulsive system.
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