Delay Dependent Stability Criteria and Stabilization for Discrete-Time Systems Via Three Terms approximation

El Mostafa El Adel (1, 2) , H El Aiss (3) , A. Hmamed (4)

1 AMU - Aix Marseille Université
2 PECASE - Pronostic-Diagnostic Et CommAnde : Santé et Energie
3 LSIS - Laboratoire des Sciences de l'Information et des Systèmes
4 LESSI-départment de physique

This paper discusses the problem of delay-dependent stability and stabilization condition for discrete-time linear systems. By employing a three-term approximation for delayed state variables, a new model transformation is developed, which has a smaller approximation error than the two-term approach. By using scaled small gain theorem and an appropriate Lyapunov-Krasovskii functional, new delay-dependent stability conditions are proposed and formulated as linear matrix inequalities (LMIs). Before the end, a state feedback controller has investigated in the stabilization of discrete linear systems. Finally, numerical examples are presented to illustrate the effectiveness of the proposed method.

Keywords: Time- Delay system; Scaled Small Gain Theorem; Linear Matrix Inequality (LMI); Discrete time delay

Domains: Engineering Sciences [physics]; Engineering Sciences [physics]; Automatic

El Mostafa El Adel, H El Aiss, A. Hmamed. Delay Dependent Stability Criteria and Stabilization for Discrete-Time Systems Via Three Terms approximation. Journal of Control Engineering and Applied Informatics, 2017, 19, pp.3 - 12. ⟨hal-02080069⟩