On Non-Overshooting Conditions for Discrete-Time Switched Linear Systems: The Multi-Input Case

The non-overshooting conditions measured by the state/output 2-norm of discrete-time switched linear systems(DTSLS) are investigated in this paper. A sufficient and necessary condition for state non-overshooting of discrete-time linear time invariant(LTI) systems is firstly derived, and the non-overshooting region, which is a pair of zero-symmetrical cones, is defined and analyzed. Adopting the idea of dividing the state space into distinct non-overshooting regions, some state non-overshooting conditions for DTSLS are addressed. The output non-overshooting problem, which is more complex, is solved in a similar way, and several output non-overshooting conditions are established. Finally, an illustrative example is given to verify the proposed conditions.