Delay-dependent robust stability and l2-gain analysis of a class of nonlinear time-delay systems

Authors:
Daniel F. Coutinho;Carlos E. de Souza
Affiliations:
Group of Automation and Control Systems, PUC-RS, Av. Ipiranga 6681, Porto Alegre, RS 90619-900, Brazil;Department of Systems and Control, LNCC/MCT, Av. Getúlio Vargas 333, Petrópolis, RJ 25651-075, Brazil
Venue:
Automatica (Journal of IFAC)
Year:
2008

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Abstract

A convex approach to robust regional stability analysis of a class of nonlinear state-delayed systems subject to convex-bounded parameter uncertainty is proposed. Delay-dependent conditions are developed to ensure system robust local stability and obtain an estimate of a domain of attraction of the origin inside a given polytopic region of the state-space. This approach is then extended to provide a delay-dependent solution to the problem of @?"2-gain analysis. The proposed approach is based on a Lyapunov-Krasovskii functional with polynomial dependence on the system state and uncertain parameters and is formulated in terms of linear matrix inequalities. Numerical examples illustrate the potentials of the derived results.