Integral Characterizations of Uniform Asymptotic and Exponential Stability with Applications
Copyright policy )Integral Characterizations of Uniform Asymptotic and Exponential Stability with Applications
Integral characterizations of uniform global asymptotic stability (UGAS) and uniform global exponential stability (UGES) for time-varying differential inclusions are proved. These integral characterizations are used to conclude UGAS from uniform global stability (UGS) and suitable properties of the derivatives of a family of functions. As a corollary, a generalization of a theorem of Matrosov (on the use of a differentiable auxiliary function to conclude UGAS) is obtained. Moreover, it is shown how one can conclude UGAS from UGS for the system and UGAS for a system related to the original system through injection of an weakly uniformly integrable output function.
- Russian Academy of Sciences Russian Federation
- French National Centre for Scientific Research France
- University of California, Santa Barbara United States
- Institute of Problems of Mechanical Engineering Russian Federation
- Supélec France
Asymptotic stability in control theory, asymptotic stability, integral characterizations, weakly uniformly integrable output function, differential inclusions, output injection, Matrosov's theorem, Ordinary differential inclusions
Asymptotic stability in control theory, asymptotic stability, integral characterizations, weakly uniformly integrable output function, differential inclusions, output injection, Matrosov's theorem, Ordinary differential inclusions
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