In this paper, explicit closed form expressions of nonsmooth strict Lyapunov tunctlons for impulsive hybrid time-varying systems with discontinuous right-hand side is provided. Lyapunov functions are expressed in term...In this paper, explicit closed form expressions of nonsmooth strict Lyapunov tunctlons for impulsive hybrid time-varying systems with discontinuous right-hand side is provided. Lyapunov functions are expressed in terms of known nonstrict Lyapunov functions for the dynamics and finite sums of persistency of excitation parameters.展开更多
In this paper,input-to-state stability of nonlinear time-delay systems on time scales is investigated.Due to the advantages of the strict Lyapunov functionals in uncertainty quantification and robustness analysis,one ...In this paper,input-to-state stability of nonlinear time-delay systems on time scales is investigated.Due to the advantages of the strict Lyapunov functionals in uncertainty quantification and robustness analysis,one always prefers to construct the strict Lyapunov functionals to analyse stability of time-delay systems.However,it may be not an easy task to do this for some timedelay systems.This paper proposes an input-to-state stability theorem based on a time-scale uniformly asymptotically stable function.The advantage of this theorem is that it is dependent on the non-strict Lyapunov functional,whose time-scale derivative can be non-negative on some time intervals.Then,some approaches are established to construct the strict Lyapunov functionals based on the non-strict ones.It is shown that input-to-state stability theorems can be also formulated in terms of these strict Lyapunov functionals.Finally,to illustrate the effectiveness of the main results,an example is given.展开更多
文摘In this paper, explicit closed form expressions of nonsmooth strict Lyapunov tunctlons for impulsive hybrid time-varying systems with discontinuous right-hand side is provided. Lyapunov functions are expressed in terms of known nonstrict Lyapunov functions for the dynamics and finite sums of persistency of excitation parameters.
基金This work was supported by the National Natural Science Foundation of China[61873150]the China Postdoctoral Science Foundation[2020M672110].
文摘In this paper,input-to-state stability of nonlinear time-delay systems on time scales is investigated.Due to the advantages of the strict Lyapunov functionals in uncertainty quantification and robustness analysis,one always prefers to construct the strict Lyapunov functionals to analyse stability of time-delay systems.However,it may be not an easy task to do this for some timedelay systems.This paper proposes an input-to-state stability theorem based on a time-scale uniformly asymptotically stable function.The advantage of this theorem is that it is dependent on the non-strict Lyapunov functional,whose time-scale derivative can be non-negative on some time intervals.Then,some approaches are established to construct the strict Lyapunov functionals based on the non-strict ones.It is shown that input-to-state stability theorems can be also formulated in terms of these strict Lyapunov functionals.Finally,to illustrate the effectiveness of the main results,an example is given.
