Finite-time control for linear systems with impulse control

This paper deals with finite-time stabilization and finite-time boundedness control problems for continuous-time linear time-varying systems with impulse control, which control is governed by discrete-time linear time-varying systems. Sufficient conditions are given for the existence of observer-based output feedback controllers that make a system finite-time stable and finite-time bounded, in terms of differential-difference linear matrix inequalities (DDLMIs). Assuming periodic solutions of the DDLMIs, numerically tractable design conditions for impulse control are given by LMIs. Numerical examples illustrate the design methods of observer-based output control as well as state feedback control.