Criteria for robust absolute stability of time-varying nonlinear continuous-time systems

The present paper establishes results for the robust absolute stability of a class of nonlinear continuous-time systems with time-varying matrix uncertainties of polyhedral type and multiple time-varying sector nonlinearities. By using the variational method and the Lyapunov Second Method, criteria for robust absolute stability are obtained in di1erent forms for the given class of systems. Speci2cally, the parametric classes of Lyapunov functions are determined which de2ne the necessary and su3cient conditions of robust absolute stability. The piecewise linear Lyapunov functions of the in2nity vector norm type are applied to derive an algebraic criterion for robust absolute stability in the form of solvability conditions of a set of matrix equations. Several simple su3cient conditions of robust absolute stability are given which become necessary and su3cient for special cases. Two examples are presented as applications of the present results to a particular second-order system and to a speci2c class of systems with time-varying interval matrices in the linear part. ? 2002 Published by Elsevier Science Ltd.