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Variable structure control of dynamical systems with mismatched norm-bounded uncertainties: an LMI approach. (English) Zbl 1017.93024
A class of linear control systems is considered in the presence of mismatched norm-bounded time-varying uncertainties in the state space as well as in the input matrix. Under suitable assumptions, a sufficient condition for the existence of a linear sliding surface guaranteeing asymptotic stability of the reduced-order equivalent sliding mode dynamics is proved. This condition is expressed in terms of linear matrix inequalities. The matrix solutions to these inequalities are used for an explicit parameterization of the sliding surface and of the switched feedback control strategy. An illustrative design example is also presented.

93B12 Variable structure systems
93B40 Computational methods in systems theory (MSC2010)
15A39 Linear inequalities of matrices
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