Robust stabilisation for a class of time-delay systems with triangular structure

The state-feedback control problem for a class of time-delay systems is investigated. The considered nonlinear systems have a triangular structure. By constructing a novel Lyapunov- Krasovskii functional, an adaptive state-feedback controller is designed via a backstepping method. The resulting closed-loop system is proved to be stable in the sense of uniform ultimate boundedness. Simulations are performed to verify the effectiveness of the proposed method.

[1]  Peng Shi,et al.  Robust backstepping control for a class of time delayed systems , 2005, IEEE Transactions on Automatic Control.

[2]  Huijun Gao,et al.  Robust L/sub 2/-L/sub /spl infin// filtering for uncertain systems with multiple time-varying state delays , 2003 .

[3]  Vladimir L. Kharitonov,et al.  Stability of Time-Delay Systems , 2003, Control Engineering.

[4]  Shuzhi Sam Ge,et al.  Adaptive neural network control of nonlinear systems with unknown time delays , 2003, IEEE Trans. Autom. Control..

[5]  Guo-Ping Liu,et al.  Delay-dependent robust stability criteria for uncertain neutral systems with mixed delays , 2004, Syst. Control. Lett..

[6]  James Lam,et al.  Robust energy-to-peak filter design for stochastic time-delay systems , 2006, Syst. Control. Lett..

[7]  Mrdjan Jankovic,et al.  Control Lyapunov-Razumikhin functions and robust stabilization of time delay systems , 2001, IEEE Trans. Autom. Control..

[8]  Shuzhi Sam Ge,et al.  Robust adaptive control of nonlinear systems with unknown time delays , 2004, Proceedings of the 2004 IEEE International Symposium on Intelligent Control, 2004..

[9]  Sing Kiong Nguang,et al.  Robust stabilization of a class of time-delay nonlinear systems , 2000, IEEE Trans. Autom. Control..

[10]  Claude H. Moog,et al.  Input-output feedback linearization of time-delay systems , 2004, IEEE Transactions on Automatic Control.

[11]  Huijun Gao,et al.  Delay-dependent output-feedback stabilisation of discrete-time systems with time-varying state delay , 2004 .

[12]  Songjiao Shi,et al.  Output feedback stabilization for a class of stochastic time-delay nonlinear systems , 2003, IEEE Trans. Autom. Control..

[13]  Martín Velasco-Villa,et al.  The disturbance decoupling problem for time-delay nonlinear systems , 2000, IEEE Trans. Autom. Control..

[14]  Yong He,et al.  Delay-dependent stability criteria for linear systems with multiple time delays , 2006 .

[15]  Changchun Hua,et al.  Comments on "State feedback stabilization for a class of stochastic time-delay nonlinear systems" , 2004, IEEE Trans. Autom. Control..

[16]  Tielong Shen,et al.  Adaptive feedback control of nonlinear time-delay systems: the LaSalle-Razumikhin-based approach , 2005, IEEE Transactions on Automatic Control.

[17]  Panagiotis D. Christofides,et al.  Non-linear feedback control of parabolic partial differential difference equation systems , 2000 .

[18]  Peng Shi,et al.  Robust stabilization of a class of nonlinear time-delay systems , 2004, Appl. Math. Comput..

[19]  Miroslav Krstic,et al.  Nonlinear and adaptive control de-sign , 1995 .

[20]  Shengyuan Xu,et al.  New Exponential Estimates for Time-Delay Systems , 2006, IEEE Transactions on Automatic Control.