Robust L₁ model reduction for uncertain stochastic systems with state delay

This paper investigates the problem of robust L₁ model reduction for continuous-time uncertain stochastic systems with state delay. For a given mean-square stable system, our purpose is to construct reduced-order systems, such that the error system between the two models is mean-square asymptotically stable and has a guaranteed L₁ performance. The peak-to-peak gain criterion is first established for stochastic systems with state delay, and the corresponding model reduction problem is solved by using projection lemma. 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. In addition, the development of delay-free reduced-order model is also presented. The efficiency of the proposed methods is demonstrated via a numerical example.