Observer Design with Guaranteed RMS Gain for Discrete-Time LPV Systems with Markovian Jumps

In this paper 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 feasibility of a family of parameter-dependent 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 a linear parameter-varying plant whose state measurements are available through a lossy Bernoulli channel. Two numerical examples illustrate the results. Copyright (C) 2008 John Wiley & Sons, Ltd.