Time-varying gain controller synthesis of piecewise homogeneous semi-Markov jump linear systems

Abstract

This paper is devoted to the time-varying gain controller synthesis problem for a class of discrete-time piecewise homogeneous semi-Markov jump linear systems (SMJLSs). Both sojourn-time probability mass functions and embedded Markov chain transition probability are simultaneously regulated by high-level Markov chain, which leads to a more general piecewise homogeneous semi-Markov kernel. A novel class of multivariate-dependent Lyapunov function is constructed, which is mode-dependent, elapsed-time-dependent, and variation-dependent. The objective of this paper is to design two classes of time-varying gain controllers, i.e., elapsed-time-dependent controller and finite memory controller under bound sojourn time. Numerically testable stabilization criteria are established for discrete-time piecewise homogeneous SMJLSs via the proposed novel Lyapunov function and two classes of controllers. Furthermore, two desired stabilizing controllers are designed such that the closed-loop system is mean-square stable. Finally, the proposed control strategies are applied to a numerical example and a practical example of solar thermal receiver to show the effectiveness and applicability of the theoretical results.