Abstract
The Badreddin-Mansour and balanced procedures of model reduction of discrete time systems are compared. For this purpose, time response errors of both the techniques are utilized. The relationship between two different reduced models arising from the balanced realization, along with their lattice realizations, is obtained. The 2D Badreddin-Mansour reduction procedure is extended to the 2D MIMO discrete time systems utilizing two new canonical forms. It is shown that in case of MIMO separable systems, the reduced model preserves stability. A comparative study of the two canonical forms is also given. Several important properties of 2D gramians and the balanced realization are derived. Through a counterexample, the conjecture that the reduced model will remain stable is proven invalid. Stability properties of the reduced model are looked into. In case of 2D separable systems, several interesting results regarding the gramians, norms, stability, and minimality are derived. An error bound for the frequency response is also presented. The computation of 2D gramians is investigated. For separable systems, this is possible through the solution of two pairs of Lyapunov equations. For non-separable systems, an efficient technique to compute the 2D gramians is developed. The controllability and observability gramians of a certain type of retarded delay differential systems are defined. The notion of canonical realization, balanced realization, and a method of effective model reduction are then developed.