Stability analysis of stochastic scalar Markovian jump systems with sample switching and state signals

This paper investigates the stability of scalar stochastic Markovian jump systems with sampled switching and state signals. The analysis of the system is complicated and difficult due to the fact that both states and modes are sampled. In order to clearly analyse these factors, a comparison method based on the solution of auxiliary functions is proposed to solve the problem of sampling both modes and states. Some novel amplification techniques are also proposed to finally establish the linear inequalities conditions. A numerical example is used to illustrate the effectiveness and superiority of these methods.

I. INTRODUCTION

It is well known that stochastic systems are dynamic systems [1], [2] and they are often used to deal with problems with sudden changes in structure and parameters. Therefore, many real-world problems are modelled by it. With the extensive development of stochastic systems, they have been used in the economy, power systems , manufacturing systems and so on [3] –[6]. Meanwhile, the stability problem of stochastic systems has been solved in recent years, where the stability of the system guaranteed by the drift term controller can be understood from [7] and the stability of the system guaranteed by the diffusion term controller can be understood from [8]. Also, [8] illustrates the advantages of controllers with diffusion terms compared to controllers with drift terms. In other words, the stochastic controller is the one that has more advantages than the controller with the diffusion term.