Finite‐time stability for time‐varying nonlinear impulsive systems

Abstract

This paper investigates the finite‐time stability (FTS) for time‐varying nonlinear impulsive systems. We provide several Lyapunov‐based theorems to ensure the FTS property, where three types of impulses including stabilizing impulses, destabilizing impulses, and multiple impulses are fully considered. The relation of the settling‐time and the impulse sequences is established. It shows that the settling‐time of the system can be shortened for the stabilizing impulses and be postponed for the destabilizing ones. In particular, under the effect of multiple impulses, the settling‐time estimation is derived via a sequence division method. Moreover, we apply the theoretical results to the control problem of coupled impulsive neural networks (CINNs) involving time‐varying uncertainties, where the control scheme is designed to guarantee the FTS of the considered systems. The effectiveness of presented results is illustrated by three simulation examples.

Effect of saturation structure on finite-time stabilization of nonlinear systems with impulsive disturbance

“…In the sense of finite time, there are some interesting results of FTS criteria for nonlinear systems with impulsive disturbance, such as [23] for state-dependent impulses and [24] for state-independent impulses. Subsequently, these results were extended to time-varying nonlinear impulsive systems [25], impulsive memristor-based neural networks [26], and delayed complex dynamical networks [27], and so on. It is worth noting that these existing results are all based on the desired control input without saturation structure.…”

“…In [24], some FTS results were established by a class of constrained impulse time sequences and the estimation of the settling-time was derived. Later, these results were not only extended to time-varying nonlinear impulsive systems by constructing a time-varying differential inequality of Lyapunov function, such as [25], but also applied to finite-time synchronization of complex dynamical networks, such as [26] and [27]. However, it is worth noting that the existing results in [24][25][26][27] are all based on the idealized environment that the control input in transmission is not limited by the physical constraints and always available.…”

“…Later, these results were not only extended to time-varying nonlinear impulsive systems by constructing a time-varying differential inequality of Lyapunov function, such as [25], but also applied to finite-time synchronization of complex dynamical networks, such as [26] and [27]. However, it is worth noting that the existing results in [24][25][26][27] are all based on the idealized environment that the control input in transmission is not limited by the physical constraints and always available. Indeed, in practical applications, the actual control input is inevitably constrained by saturation structure, see [28][29][30].…”

Finite-Time Stability and Instability of Nonlinear Impulsive Systems

“…Recently, finite-time stability of impulsive systems has also attracted lots of attention (e.g., [3,11,[17][18][19][20][21][22]), because comparing with infinite-time stable system, the finite-time stable system has faster convergence, better robustness and better disturbance rejection (see [2,25]). Meanwhile, finite-time stability has rich applications in practical systems, such as spacecraft system [4], continuously stirred tank reactor system [7] and mechanical system [10].…”

Finite-time energy-to-peak control for Markov jump systems with pure time delays

“…Feng et al 39 considered the input-output FTS for a type of switched system, and some sufficient theorems were obtained for the system. The readers can refer to references [40][41][42] for more results about FTS. Thus, if the FTS is introduced in the control of MJSs with PTD, some improved performances can be expected to be obtained.…”