Robust Kalman filter design for Markovian jump linear systems with norm-bounded unknown nonlinearities

This paper considers the problems of stability and filtering for a class of linear hybrid systems with nonlinear uncertainties and Markovian jump parameters. The hybrid system under study involves a continuous-valued system state vector and a discrete-valued system mode. The unknown nonlinearities in the system are time varying and norm bounded. The Markovian jump parameters are modeled by a Markov process with a finite number of states. First, we show the equivalence of the sets of norm-bounded linear and nonlinear uncertainties. Then, instead of the original hybrid linear system with nonlinear uncertainties, we consider the same system with linear uncertainties. By using a Riccati equation approach for this new system, a robust filter is designed using two sets of coupled Riccati-like equations such that the estimation error is guaranteed to have an upper bound.