Dynamic $L_{\text{2}}$ Output Feedback Stabilization of LPV Systems With Piecewise Constant Parameters Subject to Spontaneous Poissonian Jumps

This letter addresses the $L_{2}$ output feedback stabilization of linear parameter varying systems, where the parameters are assumed to be stochastic piecewise constants under spontaneous Poissonian jumps. We provide sufficient conditions in terms of linear matrix inequalities (LMIs) for the existence of a full-order output feedback controller. Such LMIs, however, can be computationally intractable due to the presence of integral terms. Nevertheless, we show that these LMIs can be equivalently represented by an integral-free LMI, which is computationally tractable. Finally, we provide analytical formulas to construct the controller and illustrate the applicability of the results through examples.

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