Stability Analysis And Control Method Design Of Markovian Jump System With Time-delay

In reality,due to the changes of external environment,some parameters and state of system may jump.Some jumps may result in system to be with poor performance,or even unstable.When a system jumps,it is difficult to describe it accurately by the conventional linear time-invariant system model.As a kind of stochastic system description method,Markov jump system can describe the jump system in accordance with Markov process.In recent years,the modeling,stability analysis and control of Markov jump systems have been widely studied.Considering that there are not only jumps but also time-delays in real jump systems,this paper mainly studies the stability and controller design methods of constant delay,model dependent delay and pure time-delay Markov jump systems based on Lyapunov theory and linear matrix inequality technology.Based on the energy-peak theory,a sufficient condition for energy peak stability of Markovian jump systems with constant multiple delays is obtained by selecting the appropriate Lyapunov functional,which is extended to the related theorems of system controller design.At the same time,the effectiveness of the theory is verified by an example.(2)The H? stability of Markovian jump systems with time-varying delay is studied.The sufficient conditions of system stability described by matrix inequalities and the method of H? controller design are obtained.(3)Due to the lack of the current state term for pure time-delay systems,there are relatively few stability theories based on matrix inequalities for pure time-delay systems.In this paper,the Markov jump system with pure time delay is transformed into a system description with distributed delay based on system transformation.Based on the H? stability theory and LMI technique,the sufficient conditions for system stability analysis and controller design are obtained.All the theorems are described by LMI and can be solved directly by LMI toolbox of MATLAB,which is convenient for the verification and application of the results.