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$H_\infty$ model reduction for linear time-delay systems: Continuous-time case. (English) Zbl 1022.93008
In the last decade the so-called $H_\infty$ model reduction has received much attention becoming an important research topic in applied mathematics. Basically the reduction problem involves approximating a stable system with $n$ states by another stable system with $m< n$ states such that the associated model error satisfies a prescribed $H_\infty$ norm bound constraint. Most of the results have been derived in the context of continuous and discrete-time systems without delays and parameter uncertainties. The main aim of the present paper consists in studying the problem of $H_\infty$ model reduction for linear continuous time-delay systems. The case including systems with parameter uncertainties is analysed separately. In this respect, sufficient conditions based upon linear matrix inequalities and a coupling non-convex rank constraint are proposed in order to assure the existence of the desired reduced-order model. A simple illustrative example is also given to show the effectiveness of the proposed approach.

93B11System structure simplification
93C23Systems governed by functional-differential equations
15A39Linear inequalities of matrices
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