Browsing by Author "YAHIAOUI Leila"

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    Stability radius of discrete-time systems with stochastic perturbations and their optimization by state feedback
    (University of Batna 2, 2023) YAHIAOUI Leila
    The principal objective of this dissertation is to examine the robustness stability and robustness stabilization problems for discrete-time systems on real Hilbert space. First, we consider invariant systems which are subjected to stochastic multi-perturbations. We research some features of the radius of stability through Lyapunov equations and the matching inequalities. These properties are utilized to compute the stability radius. Afterwards, we treat the optimization of the stability radius based on state feedback. Necessary and sufficient conditions are proved for stabilizing the perturbed system by feedback with norm less than a given bound. These are in terms of a discrete-time Riccati equation. We show how we can acquire the expression of the supremal stability radii based on this equation. Ultimately, we study the stability radius of discrete-time varying systems. We generalize some obtained consequences for invariant systems to the variant one. We derive bounds of the radius via the corresponding Lyapunov equation. in the end, we focus to apply the accomplished results to give conditions of the stability for periodic perturbed systems.