Robust Control For A Class Of Switched Linear Neutral Systems

As a particular class of hybrid systems, switched systems are of great significance in both theory development and engineering applications. Switched neutral systems are a broadly representative class of switched systems, which subsystems are composed of a set of continuous (or discrete) neutral systems. A switched neutral system is usually described by a set of differential (or difference) equations. A neutral system refers to the state change rate of the system is related to not only the past state, but also the change rate of the past state. Therefore, a neutral system can be regarded as a more complicated delay system in structure and character. Delay exists in practical engineering system. The research on switched delay systems is therefore of both theoretical and practical significance, which is active in recent years. As a more complex switched delay system in structure and character, the switched neutral system is attracting an increasing attention. The inherent hybrid characteristic of switched systems coupled with the complexity of neutral system itself makes the study of switched neutral systems difficult to move on.This dissertation studies the robust control problem for a class of switched linear neutral systems under the different switching strategies. The main contributions are as follows:(1) For a class of switched neutral systems with discrete time-varying delays, we design a state-dependent hysteresis switching law by using the convex combination technique and the state space partitioning method. At the same time, under the designed switching law, we obtain a delay-dependent stability criterion by using the single Lyapunov-Krasovskii functional method and introducing the free-weighting matrices.(2) For a class of switched neutral systems with discrete time-varying delays, we design a state-dependent hysteresis switching law by using the multiple Lyapunov -Krasovskii functional and the improved multiple Lyapunov-Krasovskii functional combining with the state space partitioning method. At the same time, we introduce free-weighting matrices to obtain a delay-dependent stability criterion.(3) For a class of switched neutral systems which the state can not be directly measured, we design an observer for each individual subsystem first, and then we design a state-dependent switching law and a switching feedback controller to stabilize the switched neutral system based on the designed observers. The designed switching law sufficiently considers the delayed state information. Under the designed switching law and the feedback controller, we use the multiple Lyapunov-Krasovskii functional method and introduce free-weighting matrices to analyze the stability of the closed-loop system and obtain a delay-dependent stability criterion which is given by linear matrix inequalities. At last, we extend the obtained result to the switched neutral system with uncertain time-varying structures.(4) We study the stability and L2 gain analysis of a class of switched neutral systems with mixed time-varying delays. The discrete time-varying delay and the neutral time-varying delay are different. By introducing free-weighting matrices, we obtain the stability criterion which depends on the upper bound of the discrete time-varying delay, the upper bound of the derivative of the discrete time-varying delay, the upper bound of the neutral time-varyng delay, the upper bound of the derivative of the neutral time-varying delay.(5) We study the stabilization problem for a class of switched neutral systems under sampled feedback control. Under the slow switching sense, by combining the dwell time method with the average dwell time method, we design a sampled feedback controller to stabilize a class of switched neutral systems. The asynchronization between the switching time and the sampling time would lead to mismatch between the active subsystem and its corresponding controller. This would induce instability of the whole controlled system if the mismatch lasts for a long time. In this chapter, we mainly study how to set up the relationship between the sampling period and the switching dwell time to obtain system stability.The conclusions and perspectives end this dissertation.