Continuous and Discrete State Estimation in Linear Switched Systems by Sliding Mode Observers with Residuals' Projection

This paper addresses the problem of simultaneous discrete and continuous state reconstruction in the framework of linear autonomous switched systems. Main ingredient of the approach is a stack of sliding mode observers producing suitable residual signals. These residuals are used for reconstructing the discrete state and, at the same time, for identifying the unique observer of the stack that provides an asymptotically converging estimate of the continuous state. The main result and most significant novelty of this work is a projection procedure for deriving residuals characterized by finite-time convergence. These finite-time converging projected residuals allow a faster reconstruction of the system's discrete state after the switching instants, as compared to their "unprojected" counterparts. The approach is constructively developed and theoretically substantiated along the paper, and simulation results confirm its effectiveness.