On the non-overshooting conditions for discrete-time switched linear systems

The conditions for state /output non-overshooting measured by the state /output 2-norm of discrete-time switched linear systems are addressed in this paper. As a switched linear system considered consists of several discrete-time linear time-invariant(LTI) systems, a sufficient and necessary condition for state non-overshooting of discrete-time LTI systems is derived firstly, and the non-overshooting region, which is a pair of 0-symmetrical cones, is defined and discussed. Then, using the idea of dividing the state space into distinct non-overshooting regions–a subsystem corresponding to a one, some conditions for state non-overshooting of discrete-time switched linear systems are inferred by using the well-known S-procedure. Finally, some output non-overshooting conditions were set up in a similar way.