Robust Finite-Time Stability and Stabilization of Linear Uncertain Time-Delay Systems

Robust finite-time stability and stabilization problems for a class of linear uncertain time-delay systems are studied. The concept of finite-time stability is extended to linear uncertain time-delay systems. Based on the Lyapunov method and properties of matrix inequalities, a sufficient condition that ensures finite-time stability of linear uncertain time-delay systems is given. By virtue of the results on finite-time stability, a memoryless state feedback controller that guarantees that the closed-loop system is finite time stable, is proposed. The controller design problem is solved by using the linear matrix inequalities and the cone complementarity linearization iterative algorithm. Numerical examples verify the efficiency of the proposed methods.

[1]  Gianmaria De Tommasi,et al.  Sufficient Conditions for Finite-Time Stability of Impulsive Dynamical Systems , 2009, IEEE Transactions on Automatic Control.

[2]  Carlo Cosentino,et al.  Finite-time stabilization via dynamic output feedback, , 2006, Autom..

[3]  Sophie Tarbouriech,et al.  Finite-Time Stabilization of Linear Time-Varying Continuous Systems , 2009, IEEE Transactions on Automatic Control.

[4]  Fangzheng Gao,et al.  Finite-time Stabilization of Networked Control Systems Subject to Communication Delay , 2011 .

[5]  Tadeusz Kaczorek,et al.  Practical stability and asymptotic stability of positive fractional 2D linear systems , 2010 .

[6]  Chuntao Jiang,et al.  Finite-Time Boundedness Analysis of Uncertain CGNNs with Multiple Delays , 2010, ISNN.

[7]  S. A. Milinkovic,et al.  On practical and finite-time stability of time delay systems , 1997, 1997 European Control Conference (ECC).

[8]  Zheng Yuan,et al.  Finite-time Control Synthesis of Networked Control Systems with Time-varying Delays , 2011 .

[9]  Yanjun Shen,et al.  Finite-Time Boundedness Analysis of Uncertain Neural Networks with Time Delay: An LMI Approach , 2007, ISNN.

[10]  Mohamed Ali Hammami,et al.  Practical exponential stability of perturbed triangular systems and a separation principle , 2011 .

[11]  Zhiqiang Zheng,et al.  Global finite‐time stabilization of planar nonlinear systems with disturbance , 2012 .

[12]  D. Debeljkovic,et al.  FINITE TIME STABILITY ANALYSIS OF LINEAR AUTONOMOUS FRACTIONAL ORDER SYSTEMS WITH DELAYED STATE , 2005 .

[13]  C. Lien,et al.  LMI OPTIMIZATION APPROACH FOR DELAY‐DEPENDENT H∞ CONTROL OF TIME‐VARYING DELAY SYSTEMS , 2006 .

[14]  L. Ghaoui,et al.  A cone complementarity linearization algorithm for static output-feedback and related problems , 1997, IEEE Trans. Autom. Control..

[15]  Zhao Wang,et al.  Finite-Time Tracking Control of a Nonholonomic Mobile Robot , 2008 .

[16]  Yanjun Shen,et al.  Finite-time H∞ control for linear continuous system with norm-bounded disturbance , 2009 .

[17]  D.L. Debeljkovic,et al.  Further results on the stability of linear nonautonomous systems with delayed state defined over finite time interval , 2000, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[18]  Wilfrid Perruquetti,et al.  Finite-time stability and stabilization of time-delay systems , 2008, Syst. Control. Lett..

[19]  Dingguo Jiang,et al.  Finite Time Stability of Cohen-Grossberg Neural Network with Time-Varying Delays , 2009, ISNN.

[20]  E. Moulay,et al.  Finite time stability and stabilization of a class of continuous systems , 2006 .

[21]  Weihai Zhang,et al.  Finite‐Time Stability and Stabilization of Linear Itô Stochastic Systems with State and Control‐Dependent Noise , 2013 .

[22]  Jianfeng Wang,et al.  Finite-Time Boundedness Analysis of a Class of Neutral Type Neural Networks with Time Delays , 2009, ISNN.

[23]  Francesco Amato,et al.  Finite-time control of linear systems subject to parametric uncertainties and disturbances , 2001, Autom..

[24]  S.A. Milinkovic,et al.  On practical stability of time delay systems , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).

[25]  D. Debeljkovic,et al.  Finite-time stability of delayed systems , 2000 .