Finite-Time Input/Output-to-State Stability of Impulsive Switched Nonlinear Time-Delay Systems

In this brief, we investigate the stability of impulsive switched nonlinear time-delay systems (ISNTDSs) with two asynchronous switching (TAS) phenomena. This brief extends the well-known concepts of input/output-to-state stability and integral input/output-to-state stability to finite-time control problems. In other words, two new concepts, finite-time input/output-to-state stability (FTIOSS) and finite-time integral input/output-to-state stability (FTiIOSS), are proposed for the first time, which play an important role in many practical applications. TAS phenomena refer to that the switching modes of candidate controllers does not coincide with the corresponding subsystems modes, and system impulsive instants, system switching instants are allowed to be inconsistent each other. By utilizing multiple Lyapunov-Razumikhin functions and two new switching strategies, some stability criteria on FTIOSS and FTiIOSS are presented for ISNTDSs under TAS effects. A simulation example is provided to verify the effectiveness of the developed approach.