Stability Analysis And L₂-gain Of Switched Neutral Systems With All Unstable Subsystems

Switched system is essentially a hybrid dynamical system composed of a finite number of subsystems and a logical rule that orchestrates switching between these subsystems.The dynamical behaviors of switched delay systems are affected by the interaction between the switching signals and the all unstable subsystems,therefore,are very complicated.So many problems of analysis and syntheses need to be studied.The stability analysis and L2-gain for a class of switched neutral systems with all unstable subsystems are investigated in this paper.The main contributions are as follows.Chapter 1,the basic knowledge is introduced in this chapter,such as:matrix decomposition?positive matrix?linear matrix inequality and the description of stability of switched neutral systems and L2-gain.Chapter 2 studies the stability of switched neutral systems with the unstable subsystems.Because the subsystems of the switched neutral systems are all unsta-ble.By constructing the discretized multiple Lyapunov-Krasovskii functional and resorting to the time-driven switching signals,we provide sufficient conditions for exponential stability for a class of switched neutral systems,where all subsystems are unstable.Chapter 3 studies the L2-gain of switched neutral systems with the unstable subsystems.By using average dwell time method and Lyapunov-Krasovskii func-tional method,by further allowing the Lyapunov-Krasovskii functional to increase during the running time of the active subsystem,we provide sufficient conditions in term of linear matrix inequality to guarantee the L2-gain of the switched neutral systems with all unstable subsystems.Furthermore,all the conditions are formulated in forms of a set of linear matrix inequalities which can be easily solved by using the recently developed interior point method.Finally,two numerical examples are provided to show the effectiveness of the proposed approach.