Stability Analysis And Control Synthesis Of Switched Linear Systems

There are many complex systems in the process of actual engineering and technical practice,which are composed of continuous dynamic behavior and discrete decision signals.Because the traditional control theory can't solve this kind of problem well,the switched system theory came into being under this background and has been extensively studied.This thesis proposes a new Lyapunov function approach to study the stability and control synthesis of the switched linear system.Considering the time delay between the activated modes and the corresponding controller or filter,it will be more practical to extend the above results to asynchronous switching.The main contents are outlined as follows:In the form of a positive definite convex combination,a new foreseeable Lyapunov functions that carry state information at next instant is constructed.The proposed method will carry more decision variables and relax the constraints at switching point and interval interior point.An improved criterion for the stability of discrete linear switched systems is obtained under mode-dependent average dwell time.Then,a numerical example is given to verify that the result can get a larger stability area.Further,a state feedback controller with non-weighted l₂-gain is designed by using the foreseeable Lyapunov function method,and a numerical example is given to demonstrate that the proposed method can reduce the l₂-gain to a lower level.Considering the asynchronous switching,with a mode-dependent integrated dwell time switching strategy,the state feedback controller under asynchronous switching is designed by using multiple convex Lyapunov function method.An example is given to verify the superiority of the above results.Finally,the asynchronous H_? filtering problem of discrete-time linear switched systems is investigated by the foreseeable Lyapunov function method.A foreseeable filter related to the state and noise information at the next instant is devised to ensure the resulting filtering error system is globally uniformly exponentially stable with a prescribed non-weighted l₂-gain,and then this is extended to more practical asynchronous switched systems.Some numerical examples are given to demonstrate that this method has better anti-interference ability and better filtering error response.