Mean Stability Of Uncertain Markov Jump System

Fault-prone dynamic systems may experience abrupt changes in their structure and parameters,caused by phenomena as component failures or repairs,changing subsystem interconnections,and also abrupt environmental disturbances. Then the state of the system may jump from one mode to another.If the transformation satisfies Markov stochastic process,we call this class of system Markov jump systems.In recent years,it has attract many scholars and researchers,especially in the research of stability.The paper mainly studied the jump linear system with uncertain premeters based on Lyapunov's theories of stability. The paper gives the sufficient conditions which makes the static output feedback system mean stable.The main results are listed as follows:Firstly, introduces the backgroud and development of Markov jump systems, the hot piece which are concerned,and what are being researching and what have been researched.Secondly, the paper gives the preliminaries such as basic definitions,theories and lemmas.Nextly, the paper first completes the theory3.1 in paper[32] and provids a method to solve the output feedback matrix ; then studies the mean stability of markkov jump systems whose system matrixes with uncertain parameters and both the system matrixes and control matrixes with uncertain parameters.And gives the sufficient conditions of the uncertain systems'stability.Lastly, introduces the definitions of stochastically controllability and relative conclutions and then gives the complete proof of the equality between deterministic controllability and stochastically controllability of scarlar Markov jump linear systems in paper[50].