Lyapunov-Krasovskii functional for coupled differential-functional equations

This article discusses the Lyapunov-Krasovskii functional approach for the stability problem of coupled differential-functional equations. Such systems include as special cases many types of time-delay systems, including lossless propagation model, some neutral time-delay systems and singular time-delay systems. After the general stability theory, the special case of coupled differential-difference equations is discussed, and the necessity for the existence of quadratic Lyapunov-Krasovskii functional is established. Then the stability conditions for systems with time-varying uncertainty are established based on a quadratic Lyapunov-Krasovskii functional. Discretization is used to render the stability conditions to an LMI form.

[1]  D. D. Perlmutter,et al.  Stability of time‐delay systems , 1972 .

[2]  Qing-Long Han,et al.  Robust stability of uncertain delay-differential systems of neutral type , 2002, Autom..

[3]  A. Teel.  Connections between Razumikhin-type theorems and the ISS nonlinear small gain theorem , 1998, IEEE Trans. Autom. Control..

[4]  Antonis Papachristodoulou,et al.  Positive Forms and Stability of Linear Time-Delay Systems , 2006, CDC.

[5]  Kolmanovskii,et al.  Introduction to the Theory and Applications of Functional Differential Equations , 1999 .

[6]  K. Gu.  A further refinement of discretized Lyapunov functional method for the stability of time-delay systems , 2001 .

[7]  Xinghuo Yu,et al.  A DISCRETIZED LYAPUNOV FUNCTIONAL APPROACH TO STABILITY OF LINEAR DELAY-DIFFERENTIAL SYSTEMS OF NEUTRAL TYPE , 2002 .

[8]  Jack K. Hale,et al.  Introduction to Functional Differential Equations , 1993, Applied Mathematical Sciences.

[9]  John C. Doyle.  Analysis of Feedback Systems with Structured Uncertainty , 1982 .

[10]  M. Omizo,et al.  Modeling , 1983, Encyclopedic Dictionary of Archaeology.

[11]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[12]  G. Stein,et al.  Performance and robustness analysis for structured uncertainty , 1982, 1982 21st IEEE Conference on Decision and Control.

[13]  S. Niculescu.  Delay Effects on Stability: A Robust Control Approach , 2001 .

[14]  S. Niculescu,et al.  Stability analysis of time-delay systems : A lyapunov approach , 2006 .

[15]  Sukhan Lee,et al.  Modeling, design, and evaluation of advanced teleoperator control systems with short time delay , 1993, IEEE Trans. Robotics Autom..