Finite–Time Output Stability of Impulse Switching System With Norm–Bounded State Constraint

This paper discusses the finite-time output stability (FTOS) for the impulse switching linear system (SLS) when the norm-bounded state constraint is simultaneously considered during a scheduled finite-time period. This system is a typical hybrid system whose state trajectory instantaneously jumps according to a predetermined resetting law. The sufficient conditions of both state boundedness and output stability are proposed for the SLS in finite-time period when two typical classes of input signals are involved. Based on the linear matrix inequality, the design method of a controller using state feedback is represented to ensure state boundedness and output stability concurrently for the closed-loop system, which can effectively avoid states and the output reaching large and unacceptable values at certain points in finite time. An effective solution to the controller using a linear discretization approach is also achieved. The two simulation examples verify the proposed methods.