Minimum-distance receding-horizon state estimation for switching discrete-time linear systems

State estimation is addressed for a class of discrete-time systems that may switch among different modes taken from a finite set. The system and measurement equations of each mode are assumed to be linear and perfectly known, but the current mode of the system is unknown and is regarded as a discrete state to be estimated at each time instant together with the continuous state vector. A new computationally efficient method for the estimation of the system mode according to a minimum-distance criterion is proposed. The estimate of the continuous state is obtained according to a receding-horizon approach by minimizing a quadratic least-squares cost function. In the presence of bounded noises and under suitable observability conditions, an explicit exponentially converging sequence provides an upper bound on the estimation error. Simulation results confirm the effectiveness of the proposed approach.