$\mathcal{H}_{\infty}$ Control Synthesis for Short-Time Markovian Jump Continuous-Time Linear Systems
- PDF / 800,254 Bytes
- 22 Pages / 439.37 x 666.142 pts Page_size
- 78 Downloads / 199 Views
H∞ Control Synthesis for Short-Time Markovian Jump Continuous-Time Linear Systems Weiming Xiang · Jian Xiao · Lu Han
Received: 26 July 2012 / Revised: 2 April 2013 © Springer Science+Business Media New York 2013
Abstract In many actual engineering applications, the Markovian jump among subsystems often occurs in some short finite-time intervals. For this class of Markovian jump systems, called short-time Markovian jump systems in this paper, the state boundedness during the short-time Markovian jump interval is of great interest. By introducing the concepts of finite-time stochastic stability and boundedness, sufficient conditions ensuring short-time Markovian jump system to be H∞ finite-time stochastic bounded are derived. Then, the control synthesis problem is studied, where both asymptotic stability and finite-time stochastic boundedness are considered. Finally, an LMI-based design algorithm is proposed to solve the control synthesis problem. Several numerical examples are given to illustrate the results proposed in this paper. Keywords Short-time Markovian jump system · Finite-time stochastic stability · Finite-time stochastic boundedness · H∞ finite-time stochastic control
1 Introduction Markovian jump systems, as a typical hybrid dynamical system that is composed of a family of subsystems described by differential of difference equations and transitions W. Xiang () School of Transportation and Logistics, Southwest Jiaotong University, Chengdu 610031, China e-mail: [email protected] J. Xiao · L. Han School of Electrical Engineering, Southwest Jiaotong University, Chengdu 610031, China J. Xiao e-mail: [email protected] L. Han e-mail: [email protected]
Circuits Syst Signal Process
Fig. 1 An illustrative diagram for switching only occurs in some short time interval
between the subsystems determined by a Markov chain taking values in a finite set, have attracted much attention in control theory and practice during recent decades. This class of systems was introduced by Krasovskii and Lidskii in 1961 [15] and can model stochastic systems with abrupt structural variation resulting from occurrence of some inner discrete events in the system such as failures and repairs of machine in manufacturing systems, modifications of operating point of a linearized model of a nonlinear system, and so on. A number of control problems related to Markovian jump systems have been analyzed by literature such as [9, 10, 12, 22, 40] and the references therein. In particular, with regard to Markovian jump systems with performance, there are numerous significant theory work and broad applications, for instance in [1, 11, 25–32, 36, 38] and so on. The main idea and research motivation of this paper basically come from the following points. Firstly, it worth mentioning that such an actual occurrence of inner discrete events caused by failures and repairs is often supposed to appear in some short finite-time interval, and in another most of the time the system works in a fixed mode and no Markovian jump occurs. That is to say, i
Data Loading...
