On the State Non-overshooting Conditions for Linear Discrete-Time Switched Systems

This paper presents conditions for state non-overshooting of discrete-time LTI switched systems. Based on a vector 2-norm, the state overshoot is defined, after which the conditions for state non-overshooting of discrete-time LTI systems are derived. Then, using the idea of dividing the state space into distinct regions, the state non-overshooting condition for discrete-time LTI switched systems is proposed, which is converted into a verifiable matrix inequality using the well-known S-procedure. Finally, an example is given to verify the non-overshooting conditions.