Stability analysis of impulsive switched singular systems

Abstract

This study investigates the exponential stability problems of singular impulsive switched systems. Using the switched Lyapunov function method and algebraic inequality, sufficient conditions are expressed as arbitrary and conditioned impulsive switching has been obtained. In addition, with the introduction of the impulsive controller, several exponential stability criteria are derived when the impulsive controllers are stabilising. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed criteria.

Stability and L2‐gain analysis for switched singular linear systems with jumps

“…□Remark When there is no impulsive effect considered here, the result reduces to that in . Besides in , the impulsive strength is additionally assumed to satisfy γ k ∈(0,1) to guarantee the stability. However, it is not necessary in the obtained result, and we extend the results of and to some extend.Remark Theorem does not need the condition on every impulsive interval t k − t k − 1 , k ∈ N + as but the AII.…”

“…Besides in , the impulsive strength is additionally assumed to satisfy γ k ∈(0,1) to guarantee the stability. However, it is not necessary in the obtained result, and we extend the results of and to some extend.Remark Theorem does not need the condition on every impulsive interval t k − t k − 1 , k ∈ N + as but the AII. For the impulsive signal shown in the example of , the lower bound of impulsive intervals is 0.06.…”

Stability analysis for a class of nonlinear impulsive switched systems

“…As a result, theory and methods for stability of linear or nonlinear impulsive switched systems have been extensively studied by many researchers and many research papers have been published in various academic journals, for examples, see [2,28,30,31] and the references therein.…”

RobustH∞control for switched singular linear systems with uncertainties in the derivative matrices: an improved average dwell time approach

“…This is one of the major differences between switched singular systems and switched normal systems, which make the problem for switched singular systems more difficult. There are some results on inconsistent initial condition at switching instants reported in . Some literature consider the state instantaneous jumps as known structure .…”

“…There are some results on inconsistent initial condition at switching instants reported in . Some literature consider the state instantaneous jumps as known structure . Some literature express the state instantaneous jumps based on the switched singular system matrices , and the work of authors in are further results of .…”