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Parameter-dependent Lyapunov functions for robust stability analysis of time-varying systems in polytopic domains

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3 Author(s)
Oliveira, R.C.L.F. ; Univ. of Campinas, Campinas ; de Oliveira, M.C. ; Peres, P.L.D.

The robust stability of linear continuous-time uncertain systems in polytopic domains is investigated in this paper. The uncertain parameters are assumed as time-varying with bounded rates of variation. The robust stability conditions are obtained from the definition of a Lyapunov function with a particular structure, depending on integer powers K of the dynamic uncertain matrix of the system. As a consequence, parametrized linear matrix inequalities conditions are obtained in terms of k. As K grows, the robust stability conditions can take into account bounds on the successive time-derivatives of the uncertain parameters, reducing the conservativeness of the evaluations. Numerical examples illustrate the effectiveness of the proposed methodology.

Published in:

American Control Conference, 2007. ACC '07

Date of Conference:

9-13 July 2007

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