State and Mode Estimation for Piecewise Linear Systems

This paper deals with the problem of continuous state and mode estimation for piecewise linear systems, which can be considered as a class of state-dependent linear switched systems. Some necessary and sufficient observability conditions for the mode observation, i.e. mode observability, are provided. On the other hand, some sufficient observability conditions for the continuous state are also introduced. Based on such conditions, a mode observer and a bank of continuous state observers are proposed to estimate the continuous and the mode by means of sliding-mode control techniques. Some simulation results illustrate the effectiveness of the proposed approach.