Development of Homogeneity Concept for Time-Delay Systems | Zendy

Denis Efimov | Zendy; Wilfrid Perruquetti | Zendy; JeanPierre Richard | Zendy

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Development of Homogeneity Concept for Time-Delay Systems

Author(s) -

Denis Efimov,

Wilfrid Perruquetti,

JeanPierre Richard

Publication year - 2014

Publication title -

siam journal on control and optimization

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.486

H-Index - 116

eISSN - 1095-7138

pISSN - 0363-0129

DOI - 10.1137/130908750

Subject(s) - homogeneity (statistics) , mathematics , nonlinear system , control theory (sociology) , lyapunov function , instability , computer science , physics , statistics , artificial intelligence , control (management) , quantum mechanics , mechanics

The notion of homogeneity is extended to the time-delay nonlinear systems. Applications of Lyapunov-Krasovskii functionals and Lyapunov-Razumikhin functions for stability investigation are analyzed. The notion of local homogeneity is introduced, relations between stability/instability of the locally approximating dynamics and the original time-delay system are established. A link between homogeneity and input-to-state stability is investigated. Examples of application of the proposed theory are given.

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