Hankel norm model reduction of uncertain neutral stochastic time-delay systems

This paper investigates the problems of robust Hankel norm model reduction for uncertain neutral stochastic time-delay systems with time-varying norm-bounded parameter uncertainties appearing in the state matrices. For a given mean square asymptotically stable system, our purpose is to construct reduced-order systems, which approximate the original system well in the Hankel norm sense. The Hankel norm gain criterion is first established for neutral stochastic time-delay systems, and the corresponding model reduction problem is solved by using the projection lemma, and sufficient conditions are obtained for the existence of admissible reduced-order models in terms of linear matrix inequalities (LMIs) plus matrix inverse constraints. Since these obtained conditions are not expressed as strict LMIs, the cone complementarity linearization (CCL) method is exploited to cast them into nonlinear minimization problems subject to LMI constraints, which can be readily solved by standard numerical software. The efficiency of the proposed methods is demonstrated via a numerical example.