Finite time stability and L2-gain analysis for switched linear systems with state-dependent switching

This paper considers the finite time stability and finite time boundedness problems for switched linear systems subject to L2 disturbances. Differently from the existing average dwell-time technique, state-dependent switching control strategy is used to design the switching rule, which does not require the switching instants to be known in advance. Sufficient conditions for the switched systems to be finite time stable and finite time bounded are derived; the occurrence of sliding motion will not destroy the stability with the proposed conditions. Moreover, L2-gain analysis problem is also considered. The proposed conditions are given in terms of linear matrix inequalities. Several examples are given to illustrate the effectiveness of the proposed methods.