A Novel Constraint Narrowing Technique for MIMO Unstable System

Abstract

Frequency response data collection can be a boon for modeling of MIMO uncertain plant. System stability can be assessed either by transfer function or by state-space method. Both will arrive at matrix transformation and further decision approach. Both can be considered for diagonalization of matrix. It is a proven fact that when the matrix is diagonalized the elements of the principle diagonal are the Eigen values and these Eigen values are closed loop poles from which stability can be assessed. The feature of such a diagonal matrix is that its principle diagonal elements contain gains of all the feedback paths. Singular value decomposition is used here for diagonalization. Singular value decomposition technique has been demonstrated by many authors but, application of PCA with Euclidian norm has not been paid attention so far. The systems numerical array is fed to a digital processing tool such as Mat lab and SVD-PCA (Singular Value Decomposition- Principal Component Analysis) is applied to determine the reduction of disturbance or noise and to provide minimum sensitivity and error correction. There are Hull, Box and KB consistency narrowing techniques used previously and the idea is extended further and an SVD-PCA-Norm technique which is now referred as LA criteria has been demonstrated here