Stochastic stability and stabilization of a class of piecewise-homogeneous Markov jump linear systems with mixed uncertainties.

This paper investigates the stochastic stability and stabilization problem for a general class of uncertain, continuous-time Markov jump linear systems (MJLSs). The system under consideration is a piecewise-homogenous Markovian structure subject to piecewise-constant time-varying transition rates (TRs). The time variation of the TRs is characterized by a high-level Markovian signal, which is independent from the low-level Markovian mechanism that governs the switching between the system dynamics. It is assumed that the structure is subject to mixed uncertainties in the form of additive norm-bounded terms. The uncertainties help to consider the effect of imperfections induced by modeling errors for the system dynamics and the TRs of Markovian signals of both levels. This new uncertain, two-level Markovian jump linear system is a more general model than the existing ones and is applicable to more practical situations. Besides, it is capable of being specialized to uncertain piecewise-homogeneous MJLS with arbitrarily varying TRs, as well as the uncertain time-homogeneous MJLS. The stability/stabilizability of this system is first examined by constructing a Lyapunov function which depends on both switching signals. Then, based on the analysis results, the corresponding robust controller gains are synthesized through solving a set of linear matrix inequalities (LMIs). Finally, simulation results for an industrial stirred tank reactor (CSTR) are used to demonstrate the applicability and potentials of the proposed theoretical method. Comparative simulations are also provided to show the superiority of the presented approach to the existing ones. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]