Control and Observation of Fractional Models and Applications

Abstract

Abstract : The aim of this thesis is to describe a variety of synthesis techniques concerning the observation and control laws of fractional one dimensional systems when a new models with conformable derivative and fractional-order (singular/ standard) models are discussed and also we developed a approach of H_∞ control on two-dimension system. In the first part of this thesis, we propose the application of the Sumudu transform for solving singular continuous-time linear systems based on the conformable derivative operator. Thanks to the interesting properties of the conformable Sumudu transform that we have established, a new approach is developed. Through academic and real examples, our method is compared to the existing ones, where the applicability and the accuracy of the developed process are shown. An alternative approach using the Weierstrass-Kronecker decomposition method is also given when the solution is provided with a different form. The analysis of different concepts of controllability, observability, positivity, stability and superstability of this new system are established. Additionally, In the second part of this thesis, an efficient algorithm to calculate the H_∞ norm of two-dimensional digital filters described by Roesser models is derived as an extension of the work of BOUAGADA et al. by using a para-hermitian matrix function and level sets methods of maximum singular value of the transfer function, this method converges quadratically in a few steps towards the frequency ω_1 and ω_2. We present an illustrative examples in order to show the efficiency and the accuracy of our approach.