Stability analysis for time-delay systems with partial states subject to impulsive inputs

In practice, there exist such controlled systems in which some states are often not available, not measurable or too expensive to measure. For such systems, impulsive control inputs may be exerted on the available partial states so as to stabilize the underlying systems. This paper is concerned with analyzing the stability of a class of nonlinear time-delay systems with partial states subject to impulsive inputs. The main idea is that the entire impulsively controlled system can be viewed as a hybrid one that is composed of a stable continuous subsystem and a stable impulsive subsystem. Then the analysis technique based on the new time-varying weighted Lyapunov functional/function introduced is utilized to derive sufficient conditions for exponential stability of such systems. As an illustration of the utility of the new stability criteria, the batch reactor system with the try-once-discard protocol is examined.