Fractional order time-varying-delay systems: A delay-dependent stability criterion by using diffusive representation
Résumé
The stability analysis is one of the basic problems in the fields of systems, control, and signal processing. The goal of stability analysis of time delay system is to determine the region in the delay parameter space at which the system is still stable. In this work, the stability analysis and the stabilization of fractional order time-varying delay systems modeled in the pseudo-state space are considered. First, based on the indirect Lyapunov and Lyapunov–Krasovskii approaches, sufficient time-delay-independent and dependent conditions to ensure the asymptotic stability of fractional order time-varying delay systems are provided and formulated in Linear Matrix Inequalities. Then, on the basis of the obtained sufficient conditions, the existence conditions of pseudo-state feedback controller laws are derived in matrices inequalities formulation, where the computed feedback controller must ensure the stabilization of the considered plant. Finally, numerical examples are given to illustrate the main results.