Stabilization of Stochastic Markovian Jump Systems via a Network-Based Controller

This article studies the stabilization problem of continuous-time stochastic Markovian jump systems, where the related controller is connected by a communication network. Since the controller is network based, it is natural that the related controller's information should be sampled. Particularly, both sampled state and switching signals are included in the controller, which complicates the system analysis and synthesis. An auxiliary system approach is proposed to deal with the above problems and results in a novel system model with a delayed exponential matrix. It is proven that the original system stability could be guaranteed by the constructed auxiliary system. Several stabilization results, whose controller is added in the drift section, are developed to deeply depend on the sampling interval. More extensions are further applied to a stochastic stabilization problem, whose controller is actually added in the diffusion part and act as Brownian noise. The advantages and superiorities of the methods in this article are shown by two numerical examples.

I. Introduction

It Is very well known that a network control system [1], [2] is a control system in which the elements of a control loop exchange information via a communication network. Due to the control commands transmitted in the network in the form of packets, it has advantages over traditional control strategies such as higher efficiency, flexibility, and reliability of integrated applications, but lower installation and maintenance costs. Meanwhile, it is rapidly developing in many application fields, such as driverless car systems, industrial automation, and aerospace. However, there are also some unavoidable problems, such as network-induced delay, packet loss, and denial-of-service (DoS) attacks. Presently many valuable results can be found easily, where only a few references are listed here; see, e.g., [3], [4], [5], [6], and [7]. Meanwhile, it is very common that many dynamical systems experience environmental noise, which cannot be neglected. They are usually modeled as stochastic systems, whose noise commonly satisfies the Brownian motion. Up to now, a lot of researchers have studied these systems, and many interesting results have emerged where only a few of them are mentioned in [8], [9], and [10]. Among the researched problems, the stabilization or destabilization problem closed by a stochastic controller in the diffusion part or added as a Brownian noise disturbance is characteristic. In contrast to the traditional controllers added in the drift section, the advantages of the aforementioned stochastic controller have been presented in [11] and could ensure the original state on average.