Delay-dependent and delay-independent energy-to-peak model approximation for systems with time-varying delay

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.