Computing frequency response of non‐parametric uncertainty model of MIMO systems using υ‐gap metric optimization

Abstract

This paper presents the computation of the non-parametric uncertainty model for multi input multi output (MIMO) systems, which is described by normalized coprime factors (NCF) using the frequency response data of the system. This computation is accomplished by minimizing a υ-gap metric criterion. For this purpose, the problem is formulated to a convex optimization context, such that a semidefinite programming (SDP) can be implemented. Minimization constraints and the normality constraints of coprime factors are converted to linear matrix inequalities (LMI). Thus, by convex optimization algorithms, the semidefinite programming will be optimized. The proposed method can also be used for non-square multi input multi output systems in a conservative assumption. So, through the first process of optimization, the frequency responses of the normalized coprime factors are derived. Finally, to evaluate the performance of the proposed method in the computation of the normalized coprime factors of a system, the simulated results of this method are compared with those obtained by the other methods for two types of systems.