Multiple discontinuous Lyapunov function-based stability analysis approach and reduced-order observer designs for discrete-time switched systems

In this paper, the unknown input observer design problem for the discrete-time switched system is considered. Firstly, the stability analysis based on multiple discontinuous Lyapunov function is discussed for the discrete-time switched system under the mode-dependent average dwell time concept. Then, based on such the stability analysis method, a reduced-order observer is constructed. Based on the matrix decomposition, the observer gain matrices are determined such that the influences of the unknown input can be eliminated directly in the observer constructions. Besides, based on the reduced-order observer, an unknown input algebraic reconstruction method is proposed. Finally, we give an example to show the effectiveness of the proposed methods.