The Adaptive Stabilizability Of Markov Jump System With Stochastic Disturbance

The Markov jump system is essentially a class of hybrid dynamic systems,which includes the jumping modes and continuous(or discrete)system state.With the increasing complexity of modern control systems,the system will inevitably be affected by abrupt changes caused by phenomena such as component failure,changes in the connections of the subsystems,environmental disturbance,and so on.The traditional linear system will no longer be able to satisfy the needs of control and performance,and the Markov jump system is created.Such systems often contain multiple subsystems,and different subsystems describe various dynamic behaviors of the system after abrupt changes and the Markov chain in the system describes the randomness of the jump between different subsystems.In practical application,control law design and stability analysis is one of the important research contents of Markov jumping system.The main purpose of this thesis is to discuss the adaptive stabilization of Markov jumping system,and the details are as follows:Firstly,the thesis introduces the related theory of the stability of Markov jump system and its adaptive stabilization.For discrete time Markov jump systems,by the constructing method,a necessary condition characterizing the stabilizability of the system is obtained,which hinges on the existence of a set of algebraic coupled Riccati equations.Several equivalent characterizations are also provided in this work.Secondly,in view of the continuous time Markov jump system,with the parameter identification and the Lyapunov function,a sufficient condition characterizing the stabilizability of the system is obtained,which hinges on the existence of a set of algebraic coupled Riccati equations.A constructive method for designing stabilizing feedback laws is provided in this work.Finally,for the continuous time Markov jump system,based on the analysis of the adaptive stabilization of the system,the Linear Quadratic(LQ)performance index is discussed,through the analysis and MATLAB simulation,its conclude that the index difference between the adaptive feedback control and the linear feedback control is asymptotically bounded by a constant depending on the estimation step and the stochastic disturbance priori information of the parameter set.Furthermore,the thesis analyzes the influence of the estimation step on the index.