Exponential Stability With $L_{2}$-Gain Condition of Nonlinear Impulsive Switched Systems

Abstract

In this technical note, we consider exponential stability and stabilization problems of a general class of nonlinear impulsive switched systems with time-varying disturbances. By using the switched Lyapunov function method, sufficient conditions expressed as algebraic inequality constraints and linear matrix inequalities are obtained. They ensure that the nonlinear impulsive switched systems are not only exponentially stable but also satisfy the -gain condition. Based on the stability results obtained, an effective computational method is devised for the construction of switched linear stabilizing feedback controllers. A numerical example is presented to illustrate the effectiveness of the results obtained. Index Terms-Exponentially stable, linear matrix inequality (LMI), nonlinear impulsive switched systems.

Stability analysis for a class of nonlinear impulsive switched systems

“…The main contributions of this note is that some new sufficient conditions for exponentially stability are presented. The conditions of our results are simpler than ones shown in [23] and the computational cost of solving these conditions is also lower than solving those conditions shown in [23]. Some related papers those may be helpful to readers can be found in [3-6, 9, 10, 12-14, 18-21, 25, 26].…”

“…In this note we mainly adopt the notation and terminology in [23]. The nonlinear impulsive switched systems considered in [23] can be described by…”

“…In [23], Xu and Teo considered a general class of nonlinear impulsive switched systems with nonlinear impulsive increments and presented some sufficient conditions for exponentially stability. The authors of [7,15] studied exponential stability of nonlinear impulsive switched systems with delays.…”

“…Motivated by the above mentioned works, in this note, we shall also consider stability analysis for a class of nonlinear impulsive switched systems, as in [23]. The main technique of this note is based on an original argument developed in [23], with some technical changes.…”

“…The main technique of this note is based on an original argument developed in [23], with some technical changes. The main contributions of this note is that some new sufficient conditions for exponentially stability are presented.…”