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Dissipativity analysis and synthesis of a class of nonlinear systems with time-varying delays. (English) Zbl 1169.93012

Summary: In this paper, new results are established for the delay-independent and delay-dependent problems of dissipative analysis and state-feedback synthesis for a class of nonlinear systems with time-varying delays with polytopic uncertainties. This class consists of linear time-delay systems subject to nonlinear cone-bounded perturbations. Both delay-independent and delay-dependent dissipativity criteria are established as linear matrix inequality-based feasibility tests. The developed results in this paper for the nominal system encompass available results on \(\mathcal H_{\infty }\) approach, passivity and positive realness for time-delay systems as special cases. All the sufficient stability conditions are cast. Robust dissipativity as well as dissipative state-feedback synthesis results are also derived. Numerical examples are provided to illustrate the theoretical developments.

MSC:

93C10 Nonlinear systems in control theory
93B35 Sensitivity (robustness)
93D15 Stabilization of systems by feedback
93B50 Synthesis problems
93C15 Control/observation systems governed by ordinary differential equations

Software:

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References:

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