Observer Design with Guaranteed RMS Gain for Linear Parameter Varying Jump Systems

We consider the problem of designing state observers with guaranteed power-to-power (RMS) gain, for a class of stochastic discrete-time linear systems that possess both measurable parameter variations and Markovian jumps in their dynamics. It is shown in the paper that an upper bound on the RMS gain of the observer can be characterized in terms of robust feasibility of a family of linear matrix inequalities (LMIs). Any feasible solution to these LMIs can then be used to explicitly construct a parameter-varying jump observer that guarantees the desired performance level. This design framework is then specialized to a problem of state estimation for an LPV plant whose state measurements are available trough a lossy Bernoulli channel. A numerical example illustrates the results.