Robust Kalman filter design for hybrid systems with norm-bounded unknown nonlinearities

Considers the filtering problem for a class of linear hybrid systems with nonlinear uncertainties and Markovian jump parameters. The unknown nonlinearities in the system are time-varying and norm-bounded. First, we show the equivalence of the norm bounded linear and nonlinear uncertainty sets. 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.