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A dissipative dynamical systems approach to stability analysis of time delay systems
Author(s) -
Chellaboina VijaySekhar,
Haddad Wassim M.,
Kamath Ajeet
Publication year - 2004
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.965
Subject(s) - dissipative system , exponential stability , mathematics , dynamical systems theory , dissipative operator , interconnection , stability (learning theory) , operator (biology) , control theory (sociology) , dynamical system (definition) , linear dynamical system , term (time) , quadratic equation , stability theory , mathematical analysis , linear system , computer science , control (management) , physics , nonlinear system , artificial intelligence , quantum mechanics , machine learning , repressor , computer network , chemistry , biochemistry , geometry , transcription factor , gene
In this paper the concepts of dissipativity and the exponential dissipativity are used to provide sufficient conditions for guaranteeing asymptotic stability of a time delay dynamical system. Specifically, representing a time delay dynamical system as a negative feedback interconnection of a finite‐dimensional linear dynamical system and an infinite‐dimensional time delay operator, we show that the time delay operator is dissipative with respect to a quadratic supply rate and with a storage functional involving an integral term identical to the integral term appearing in standard Lyapunov–Krasovskii functionals. Finally, using stability of feedback interconnection results for dissipative systems, we develop sufficient conditions for asymptotic stability of time delay dynamical systems. The overall approach provides a dissipativity theoretic interpretation of Lyapunov–Krasovskii functionals for asymptotically stable dynamical systems with arbitrary time delay. Copyright © 2004 John Wiley & Sons, Ltd.