Simple Stability Conditions of Linear Switched Systems with Time-Dependent Switching

In this paper, the stability of continuous-time and discrete-time linear switched systems with time-dependent switching is investigated. Solutions to the state equations are provided and sufficient conditions for the stability of such systems are established. The stability conditions presented for continuous-time systems are valid in the following cases: 1) there are no specific restrictions on the switching function if each switching interval is equal to or greater than 1 second; 2) the switching function has to be a periodic function (or a function describing permutations of identical sequences of subsystems) if at least one of the switching intervals is less than 1 second. In the case of discrete-time systems the switching function is arbitrary. The effectiveness of the presented approach is demonstrated by numerical examples.