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International Journal of Control, Vol.77, No.2, 206-215, 2004
Robust sliding mode control of non-linear systems with delay: a design via polytopic formulation
This paper outlines the possibility to control non-linear uncertain systems with single, possibly time-varying state-delay. These systems are submitted to additive perturbations ( possibly non-vanishing). The control is of sliding mode type and the sliding surface is designed to maximize the calculable set of delays which do not destabilize the relay - delay system. The way to deal with the non-linear parts of the model relies on a polytopic formulation, i.e. a decomposition into a non-linear combination of linear models, whose weighting coefficients satisfy a convex property. The conditions for the existence of the sliding regime are studied by using both a Lyapunov - Krasovskii functional and a Lyapunov Razumikhin function. The optimization procedure for the choice of the sliding surface is expressed in terms of LMIs. An example illustrates the proposed method.