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Delay-dependent and delay-independent energy-to-peak model approximation for systems with time-varying delay. (English) Zbl 1121.93020
Summary: This paper deals with the problem of computing an approximation system for a given system with time-varying delay such that the energy-to-peak gain of the error system is less than a prescribed scalar. First, a delay-dependent boundedness condition of energy-to-peak gain is given in terms of linear matrix inequalities (LMIs), which recovers the delay-independent case. Then, based on the established delay-dependent boundedness condition of energy-to-peak gain, a sufficient condition to characterize the approximation system is obtained to solve the energy-to-peak model approximation problem in the form of LMIs with inverse constraints. A number of delay-independent energy-to-peak model approximation cases are special cases of a delay-dependent approximation. An efficient algorithm is derived to obtain the approximation models. Finally, examples are employed to demonstrate the effectiveness of the model approximation algorithm.

93B30System identification
93C23Systems governed by functional-differential equations
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