Thesis /

ROMDOC-THESIS-2017-1083

Positivity in the analysis and synthesis of multidimensional systems

Şicleru, Bogdan C.
2011-09-21

Abstract: Department of Automatic Control and Computers Thesis title: Positivity in analysis and synthesis of multidimensional systems Author: eng. Bogdan C. Șicleru Advisor: Professor Bogdan Dumitrescu The purpose of this thesis is to explore the potential of positive polynomials through the characterization with positive definite matrices. As we show, algorithms based on positive polynomials can offer better results than the ones already known in the literature. The increasing usage of positive polynomials in the last decade motivated us to create POS3POLY-the first MATLAB library that can handle all types of polynomials: trigonometric, real and hybrid, the last one being the combination of the first two. Using this library the user can solve optimization problems involving positive polynomials without knowing how to implement a positive polynomial variable, thus greatly reducing the effort to implement problems with positive polynomials. The first problem reformulated with positive polynomials in this thesis is the controllability radius, i.e. the distance from an uncontrollable system to a controllable one. Our algorithm using positive polynomials is faster than the existing ones and offers good accuracy. Hybrid polynomials gave us the possibility to solve the problem of adjustable filters which until now was solved with discretization. Our method can offer the same results with lower complexity. Hybrid positive polynomials have found usage also in the analysis of the stability of systems with delays. Here we have obtained more reliable algorithm than the previous one which used discretization. Positive polynomials can also be used in the context of spatially interconnected systems. Using positive polynomials we have created an algorithm that offers a MIMO FIR filter with better stopband energy than the ones present in the literature so far. We appreciate that positive polynomials will continue to influence the world of researchers and so POS3POLY could find a place among the well known libraries used for optimization. Another subject approached in this thesis is the design of 3-D two-channel filter banks. Here, we have obtained filters with better stopband energy.

Keyword(s): Polinoame -- Teză de doctorat ; Prelucrarea semnalului -- Teză de doctorat ; Algoritmi matematici -- Teză de doctorat ; POS3POLY (biliotecă MATLAB) -- Teză de doctorat
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