Optimal multidimensional model reduction based on combined projections H₂ norm: application to continuous and discrete time systems

ABSTRACT

A comparative study of two important Model Order Reduction (MOR) systems based on internal projections and $H_2$ norm is presented. It is about Tangential interpolation and the Linear Matrix Inequalities (LMIs) optimisation based methods. In both techniques, the resulting optimal approximants of reduced order are constructed from state space projections and constrained to verify a certain $H_2$ relative error norm. In this paper, its shown the applicability of these techniques as well for the continuous time as the discrete time multidimensional systems. Since the industry has always been one of the main motivating fields for the development of MOR techniques, the present work offers an expansion to state of the art low order MOR tools and their use to any industrial process to achieve three core features: simplicity of analysis, low computation efforts and an easy and feasible control.

KEYWORDS:

• Continuous and discrete time systems
• SISO and MIMO systems
• Model Order Reduction (MOR)
• H₂ norm
• Tangential Interpolation approach
• LMIs
• optimal reduced models

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Notes on contributors

Amel B. H. Adamou-Mitiche

Amel B. H. Adamou-Mitiche received her Engineer diploma from the Ecole Nationale Polytechnique of Algiers (ENPA), Magister from the USTHB University, and the Doctorat d’Etat from the ENPA, all in Control Systems. She is a Full Professor, and leader of the research team Approximation Moderne des Systèmes Complexes of the Laboratoire de Recherche Modélisation Simulation et Optimisation des Systèmes Complexes Réels at the University of Djelfa, Algeria. Her research interests include model order reduction, State space representation, Robust modern control systems, 2D FIR and 2D IIR filters approximation, Descriptor systems approximation, Singular Systems, Generalized state space representation, and Digital image processing. She is author of a great deal of research studies published at first rank international journals, and conference proceedings.

Lahcène Mitiche

Lahcène Mitiche received his Engineer diploma, Magister, and Doctorat d’Etat in Electronics, from the Ecole Nationale Polytechnique of Algiers, Algeria. He is Full  Professor of Signal Processing and Director of the Laboratoire de Recherche Modélisation Simulation et Optimisation des Systèmes Complexes Réels, at the University of Djelfa, Algeria. His research interests include digital signal processing, model order reduction, speech modeling, modern control systems, 2D FIR and 2D IIR filters approximation, and image denoising. He is author of a great deal of research studies published at first rank international journals, and conference proceedings.