scholarly journals Strict Lyapunov functions for time-varying systems with persistency of excitation

Automatica ◽  
2017 ◽  
Vol 78 ◽  
pp. 274-279 ◽  
Author(s):  
Mohamed Adlene Maghenem ◽  
Antonio Loría
Keyword(s):  
Lyapunov Functions ◽  
Time Varying ◽  
Time Varying Systems ◽  
Persistency Of Excitation

Partial stability analysis of nonlinear time-varying impulsive systems

2019 ◽  
Vol 12 (06) ◽  
pp. 1950066
Author(s):  
Boulbaba Ghanmi
Keyword(s):  
Stability Analysis ◽  
Lyapunov Functions ◽  
Time Varying ◽  
Impulsive Systems ◽  
Partial Stability ◽  
Stability Theorems ◽  
Time Varying Systems ◽  
The Stability ◽  
Derivatives Of ◽  
Theoretical Results

This paper investigates the stability analysis with respect to part of the variables of nonlinear time-varying systems with impulse effect. The approach presented is based on the specially introduced piecewise continuous Lyapunov functions. The Lyapunov stability theorems with respect to part of the variables are generalized in the sense that the time derivatives of the Lyapunov functions are allowed to be indefinite. With the help of the notion of stable functions, asymptotic partial stability, exponential partial stability, input-to-state partial stability (ISPS) and integral input-to-state partial stability (iISPS) are considered. Three numerical examples are provided to illustrate the effectiveness of the proposed theoretical results.

Uniform Global Asymptotic Stability of Adaptively Controlled Nonlinear Systems via Strict Lyapunov Functions

2008 ◽  
Author(s):  
Fre´de´ric Mazenc ◽  
Marcio de Queiroz ◽  
Michael Malisoff
Keyword(s):  
Asymptotic Stability ◽  
Lyapunov Functions ◽  
Unknown Parameter ◽  
Time Varying ◽  
Excitation Condition ◽  
Parameter Vector ◽  
Uniform Asymptotic Stability ◽  
Asymptotic Tracking ◽  
Persistency Of Excitation ◽  
Unknown Parameter Vector

We prove global uniform asymptotic stability of adaptively controlled dynamics by constructing explicit global strict Lyapunov functions. We assume a persistency of excitation condition that implies both asymptotic tracking and parameter identification. We also construct input-to-state stable Lyapunov functions under an added growth assumption on the regressor, assuming that the unknown parameter vector is subject to suitably bounded time-varying uncertainties. This quantifies the effects of uncertainties on the tracking and parameter estimation. We demonstrate our results using the Ro¨ssler system.

scholarly journals Lyapunov functions for nonlinear time-varying systems

1968 ◽  
Vol 12 (5) ◽  
pp. 378-393 ◽  
Author(s):  
Kumpati S. Narendra ◽  
James H. Taylor
Keyword(s):  
Lyapunov Functions ◽  
Time Varying ◽  
Time Varying Systems
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