Finite Time Stability Of Positive Impulsive Switched Systems

In the stability theory of systems, there are several classical stability analyses. Such as Lyapunov stability, bounded-input-output stability, asymptotic stability. They all deal with the stability of the systems in infinite time. However, in many practical applications, when the initial condition of the systems is less than a certain number in the limited time. The state of the systems does not exceed a given threshold. Base on this, FTS is put forward.FTS is different from classical stability analysis, which is reflected in two important respects. Firstly, dealing with systems, its operation is not limited to a fixed finite time. Secondly, the system’s variable is required bounded, namely the specified range. In practical considerations, the systems variable must be located within a specific range. In this case, FTS is the only definition of theoretical and practical significance.This paper considers the finite time stability of linear system, then the concept of finite time stability is promoted to positive linear switched systems. we start from the existence of solution and use the method of solving differential equations to prove the stability of the systems. Finally, we extend the method to the finite time stability of positive impulsive switched systems.