Improved results on state estimation for switched continuous-time linear systems

This paper investigates the state estimation problem for switched linear systems involving additive disturbance and measurement noise, whose modes need not to be cooperative. Under the assumption that there exist nonsingular matrices that transform the observer error system matrices into Metzler ones, by using multiple Lyapunov functions and average dwell time method, hybrid state observers, which can produce a framer covering all possible state trajectories, are designed in two cases, that is, all the subsystems are stable and some of the subsystems may be unstable. The constructed interval observer for the considered systems are hybrid dynamical systems and the initialized states of the upper and lower observers at each switching instants are coupled, since the transformation matrices for different subsystems are different. Compared with the robust observer design for switched systems with arbitrary switching sequences in the literature, the difficulty consists in proposing new observer design conditions related to the state reset at the switching instants for switched systems under average dwell time scheme. Finally, two examples are given to show the efficiency of the proposed approach.