Adaptive stabilizing state feedback controllers of uncertain dynamical systems with multiple time delays

The problem of robust stabilization for a class of uncertain dynamical systems with multiple delayed state perturbations is considered. In this paper, it is assumed that each perturbation is bounded by a linear function of delayed state with unknown gains, and an adaptation law is proposed to estimate these unknown gains. Moreover, by making use of the updated values of these unknown bounds we propose a memoryless state feedback controller for such a class of uncertain time-delay systems. Based on Lyapunov stability theory and Lyapunov-Krasovskii functional, it is shown that the closed-loop dynamical system resulting from the proposed adaptive robust control schemes is globally stable in the sense of uniform ultimate boundedness. Finally, a numerical example is given to demonstrate the validity of the results.

[1]  Chong-Ho Choi,et al.  Adaptive regulation for a class of uncertain systems with partial knowledge of uncertainty bounds , 1993, IEEE Trans. Autom. Control..

[2]  M. Corless,et al.  Adaptive control of systems containing uncertain functions and unknown functions with uncertain bounds , 1983 .

[3]  M. Corless,et al.  Continuous state feedback guaranteeing uniform ultimate boundedness for uncertain dynamic systems , 1981 .

[4]  H. Wu,et al.  Linear and nonlinear stabilizing continuous controllers of uncertain dynamical systems including state delay , 1996, IEEE Trans. Autom. Control..

[5]  S. Gutman,et al.  Stabilization of uncertain dynamic systems including state delay , 1989 .

[6]  Hansheng Wu,et al.  Continuous adaptive robust controllers guaranteeing uniformultimate boundedness for uncertain nonlinear systems , 1999 .

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

[8]  Hansheng Wu,et al.  Exponential stability of a class of nonlinear dynamical systems with uncertainties , 1993 .

[9]  G. Leitmann,et al.  Robustness of uncertain systems in the absence of matching assumptions , 1987 .

[10]  K. Mizukami,et al.  Robust stability criteria for dynamical systems including delayed perturbations , 1995, IEEE Trans. Autom. Control..

[11]  George Leitmann,et al.  On ultimate boundedness control of uncertain systems in the absence of matching assumptions , 1982 .

[12]  Bernard Brogliato,et al.  Practical stabilization of a class of nonlinear systems with partially known uncertainties , 1995, Autom..

[13]  V. Kolmanovskii,et al.  Stability of Functional Differential Equations , 1986 .

[14]  Martin Corless,et al.  A new class of stabilizing controllers for uncertain dynamical systems , 1982, CDC 1982.

[15]  Hansheng Wu,et al.  Eigenstructure assignment-based robust stability conditions for uncertain systems with multiple time-varying delays , 1997, Autom..

[16]  K. Mizukami,et al.  Robust stabilization of uncertain linear dynamical systems with time-varying delay , 1994 .