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

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 functio...

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Bibliographic Details
Published in:Mediterranean journal of mathematics 2022-12, Vol.19 (6), Article 249
Main Authors: Damak, Hanen, Hadj Taieb, Nizar, Hammami, Mohamed Ali
Format: Article
Language:English
Subjects:
Control theory
Feedback control
Liapunov functions
Mathematics
Mathematics and Statistics
Nonlinear control
Nonlinear systems
Stability analysis
Time varying control systems
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Summary: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.
ISSN:1660-5446
1660-5454
DOI:10.1007/s00009-022-02179-z