Finite-time stabilization and boundedness of switched linear system under state-dependent switching

In this paper, finite-time stabilization and boundedness (FTSB) problems are investigated. Unlike the existing approach based on time-dependent switching strategy, in which the switching instants must be given in advance, largest region function strategy, i.e., state-dependent switching strategy, is adopted to design the switching signal. Based on multiple Lyapunov-like functions method, some sufficient conditions are provided for FTSB of switched linear system and the corresponding sliding motion problem is also considered. Finally, two examples are given to verify the efficiency of the proposed methods.