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This paper deals with the robustness of a class of discrete-time jump linear systems whose parameters are governed by a finite-state Markov chain and subject to piecewise deterministic and stochastic structured uncertainties. We establish that the exponential stability of this class is equivalent to the exponential stability of an associated class of discrete-time linear systems with no jumping parameters and subject to block diagonal deterministic and stochastic structured uncertainties. This key result is used to propose lower bounds for what we define as the stability radii with respect to this class of perturbation structures. The optimization problem of the stability radii that can be achieved by dynamic output feedback is also discussed and sufficient conditions are derived for the existence of stabilizing compensator which ensures that the stability radius is above a given level, via the resolution of parameterized matrix inequalities.

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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.

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