Delay-Dependent Stabilizability of 2D Delayed Continuous Systems with Saturating Control

This paper deals with the problem of stability and stabilization of 2D delayed continuous systems with saturation on the control. Improved delay depedent stability condition taken from recent literature is firstly extended to the case of 2D systems. Second, delay depedent stabilizability condition is deduced. The synthesis of stabilizing saturating state feedback controllers for such systems is then given. A set of allowed delays for both directions of the state is computed. All involved conditions are given under LMI's formalism. Examples are worked to show the effectiveness of the approach. Response to Reviewers: Powered by Editorial Manager® and Preprint Manager® from Aries Systems Corporation Noname manuscript No. (will be inserted by the editor) Delay-dependent stabilizability of 2D delayed continuous systems with saturating control Mohamed Benhayoun, Fouad Mesquine, Abdellah Benzaouia the date of receipt and acceptance should be inserted later Abstract 1 This paper deals with the problem of stability and stabilization of 2D delayed continuous systems with saturation on the control. Improved delay dependent stability condition taken from recent literature is firstly extended to the case of 2D systems. Second, delay dependent stabilizability condition is deduced. The synthesis of stabilizing saturating state feedback controllers for such systems is then given. A set of allowed delays for both directions of the state is computed. All involved conditions are given under LMIs formalism. Examples are worked to show the effectiveness of the approach.1 This paper deals with the problem of stability and stabilization of 2D delayed continuous systems with saturation on the control. Improved delay dependent stability condition taken from recent literature is firstly extended to the case of 2D systems. Second, delay dependent stabilizability condition is deduced. The synthesis of stabilizing saturating state feedback controllers for such systems is then given. A set of allowed delays for both directions of the state is computed. All involved conditions are given under LMIs formalism. Examples are worked to show the effectiveness of the approach. Key-words: 2D Delayed continuous systems, Roesser model, Delay-dependent conditions, State feedback control, Lyapunov-Krasovskii functional, Control saturation, LMIs.