TAILIEUCHUNG - Practical stability of linear time-varying delay systems

This paper is concerned with the problem of practical stability of linear time-varying delay systems in the presence of bounded disturbances. Based on some comparison techniques associated with positive systems, explicit delay-independent conditions are derived for determining a neighborhood of the origin which ultimately bounds all state trajectories of the system. | 12 I Ha Noi MeTROPLOLiTAN University practical stability of linear time-varying delay systems Le Van Hien Hanoi National University of Education Abstract This paper is concerned with the problem of practical stability of linear timevarying delay systems in the presence of bounded disturbances. Based on some comparison techniques associated with positive systems explicit delay-independent conditions are derived for determining a neighborhood of the origin which ultimately bounds all state trajectories of the system. Keywords Practical stability time-varying delay Metzler matrix. Email hienlv@ Received 29 July 2018 Accepted for publication 15 October 2018 1. INTRODUCTION In practical systems there usually exists an interval of time between a stimulation and the system response 1 . This interval of time is often known as time delay of a system. Since time-delay unavoidably occurs in engineering systems and usually is a source of poor performance oscillations or instability 2 the problem of stability analysis and control of time-delay systems is essential and of great importance for theoretical and practical reasons 3 . This problem has attracted considerable attention from the mathematics and control communities see for example 4-10 . When considering long-time behavior of a system the framework of Lyapunov stability theory and its extensions for time-delay systems the Lyapunov-Krasovskii and Lyapunov-Razumikhin methods have been extensively developed 3 . However realistic systems usually exhibit characteristics for which theoretical definitions in the sense of Lyapunov can be quite restrictive 11 . Namely the desired state of a system may be mathematically unstable in the sense of Lyapunov but the response of the system oscillates close enough to this state for its performance to be considered as acceptable. Furthermore in many control problems especially for systems that may lack an equilibrium point due to the presence of disturbances or constrained .

• Vật lý
• Practical stability
• Time varying delay
• Metzler matrix
• Positive systems
• Explicit delay independent
• systems
• controls
• a practical approach to signal
• physical systems
• exponential stability
• system transfer funtion