|Stochastic Stability, L1-gain and Control Synthesis for Positive Semi-Markov Jump Systems
Longjiang Zhao, Wenhai Qi*, Lihua Zhang, Yonggui Kao, and Xianwen Gao
International Journal of Control, Automation, and Systems, vol. 16, no. 5, pp.2055-2062, 2018
Abstract : "This paper treats the problems of stochastic stability, L1-gain and control synthesis for positive semi-
Markov jump systems (S-MJSs). The system under consideration involves semi-Markov stochastic process related
to Weibull distribution. The main motivation for this paper is that the positive condition sometimes needs to be
considered in S-MJSs and the controller design methods in the existing works have some conservation. To deal
with these problems, some sufficient conditions for stochastic stability of positive S-MJSs are established by implying
the linear co-positive Lyapunov function. Then, some sufficient conditions for L1-gain constraint are also
presented, upon which, a state feedback controller is designed by decomposing the controller gain matrix such
that the resulting closed-loop system is positive and stochastically stable with L1-gain performance in the form of
standard linear programming (LP). The advantages of the new framework lie in the following facts: (1) the weak
infinitesimal operator is derived for S-MJSs under the constraint of positive condition and (2) the less conservative
stabilizing controller is designed to achieve the desired control performance. Finally, numerical examples are given
to demonstrate the validity of the main results."
Semi-Markov jump systems, state feedback controller, stochastic stability.