Finite-time stabilization and $H_\infty$ control of nonlinear delay systems via output feedback

Ta T. H. Trang (1) , Vu N. Phat (1) , Samir Adly (2)

1 VAST - Vietnam Academy of Science and Technology
2 XLIM-MATHIS - Mathématiques & Sécurité de l'information

This paper studies the robust finite-time Ho., control for a class of nonlinear systems with time-varying delay and disturbances via output feedback. Based on the Lyapunov functional method and a generalized Jensen integral inequality, novel delay-dependent conditions for the existence of output feedback controllers are established in terms of linear matrix inequalities (LMIs). The proposed conditions allow us to design the output feedback controllers which robustly stabilize the closed-loop system in the finite-time sense. An application to $H_\infty$ control of uncertain linear systems with interval time-varying delay is also given. A numerical example is given to illustrate the efficiency of the proposed method.

Mots clés: linear matrix inequality; finite-time stabilization; $H_\infty$ control; output feedback; time-varying delay; Lyapunov function

Domaines: Optimisation et contrôle [math.OC]

Ta T. H. Trang, Vu N. Phat, Samir Adly. Finite-time stabilization and $H_\infty$ control of nonlinear delay systems via output feedback. Journal of Industrial and Management Optimization, 2016, 12 (1), pp.303-315. ⟨10.3934/jimo.2016.12.303⟩. ⟨hal-01313201⟩