Model Approximation of 2-D State-Delayed Systems

Abstract

This chapter is concerned with the $\mathcal {H}_{\infty }$ model approximation problem for 2-D discrete state-delayed systems. Our attention is focused on the construction of a reduced-order model, which can approximates the original system well in an $\mathcal {H}_{\infty }$ norm sense. Sufficient conditions are first derived for the existence of admissible reduced-order solutions, and then the solvability conditions for the reduced-order models are established by utilizing the projection approach. Since these obtained conditions are not expressed as strict LMIs, the cone complementary linearization (CCL) algorithm is exploited to cast them into a sequential minimization problem subject to LMI constraints, which can be readily solved in standard numerical software. Moreover, the obtained results are further extended to the multiple delays case.