Universal adaptive stabilization for a class of multivariable Markovian jump linear systems with partially unknown transition rates

Abstract

Abstract In this paper, the problem of universal adaptive stabilization is investigated for a class of multi-input multi-output Markovian jump linear systems (MJLSs) with partially unknown transition rates (TRs). The class of systems that we are considering is characterized only by some structural assumptions. Firstly, we show the high-gain stochastic stabilizability, that is, any system belonging to this class can be stabilized by a mode-dependent output feedback controller, provided that the proportional gain for every mode is sufficiently large. Moreover, a universal adaptive high-gain controller, which is not based on identification or any estimation algorithms, is presented. It is shown that this controller ensures the convergence and the boundedness of the closed-loop system signals in the mean square sense. Finally, simulation results are given to illustrate the performance and effectiveness of the proposed approaches. MJLSs, high-gain stabilizability, universal adaptive control, output feedback, partially unknown TRs.