On Input-to-State Practical h-Stability for Nonlinear Time-Varying Systems

被引：0
|
作者：
Hanen Damak
Nizar Hadj Taieb
Mohamed Ali Hammami
机构：
[1] University of Sfax,Faculty of Sciences of Sfax, Department of Mathematics
来源：
Mediterranean Journal of Mathematics | 2022年 / 19卷
关键词：
Input-to-state practical ; -stability (; -ISpS); integral input-to-state practical ; -stability (; -iISpS); Lyapunov theory; nonlinearsystems; 34D10; 34D23; 93C10; 93D15;
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摘要：
In this paper, we introduce a new concept of input-to-state practical h-stability (h-ISpS) and integral input-to-state practical h-stability (h-iISpS) for nonlinear time-varying systems. Necessary and sufficient conditions for h-ISpS and h-iISpS are given based on indefinite Lyapunov functions. The practical h-stability analysis is accomplished with the help of scalar practical h-stable functions. Our main result provides conditions for h-ISpS of perturbed, cascaded and interconnected systems. Furthermore, a feedback control law is provided for a class of nonlinear control systems by which the closed-loop system is h-iISpS with respect to disturbances acting in the input. Some examples are given to illustrate the obtained results.
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