An LMI Approach for the Stabilization of Discrete-Time Delay Nonlinear Systems Using Backstepping

In this paper, an-LMI approach is utilized for the stabilization of Discrete-Time Delay Nonlinear Systems (DTDNS). The delay provided is state-delay. The control criterion is derived in terms of linear matrix inequalities (LMI's). The controller is designed by making use of back stepping technique. By choosing an appropriate Lyapunov function, some mathematical manipulations have been carried out to deduce simple LMI condition for asymptotic stabilization. The effectiveness and the applicability of the proposed control law is verified through simulation.

[1]  S. Ge,et al.  Adaptive neural control of nonlinear time-delay systems with unknown virtual control coefficients , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[2]  Emilia Fridman,et al.  New Lyapunov-Krasovskii functionals for stability of linear retarded and neutral type systems , 2001, Syst. Control. Lett..

[3]  M. Mahmoud.  Robust Control and Filtering for Time-Delay Systems , 2000 .

[4]  Shunian Zhang,et al.  Stability of neutral delay difference systems , 2001 .

[5]  Magdi S. Mahmoud,et al.  Robust H control of discrete systems with uncertain parameters and unknown delays , 2000, Autom..

[6]  Emilia Fridman,et al.  An improved stabilization method for linear time-delay systems , 2002, IEEE Trans. Autom. Control..

[7]  Magdi S. Mahmoud.  Linear parameter-varying discrete time-delay systems: Stability and l 2-gain controllers , 2000 .

[8]  H. Trinh,et al.  A memoryless state observer for discrete time-delay systems , 1997, IEEE Trans. Autom. Control..

[9]  E. Fridman,et al.  An LMI approach to stability of discrete delay systems , 2003, 2003 European Control Conference (ECC).

[10]  W. Kwon,et al.  Delay-dependent robust stabilization of uncertain discrete-time state-delayed systems , 2002 .

[11]  M. Aldeen,et al.  A memoryless reduced-order state observer for discrete-time systems with multiple delays , 1997, 1997 European Control Conference (ECC).

[12]  Xi Li,et al.  Criteria for robust stability and stabilization of uncertain linear systems with state delay , 1997, Autom..

[13]  Emilia Fridman,et al.  Delay-Dependent H∞ Control of Uncertain Discrete Delay Systems , 2005, Eur. J. Control.

[14]  Vladimir L. Kharitonov,et al.  Lyapunov-Krasovskii approach to the robust stability analysis of time-delay systems , 2003, Autom..

[15]  U. Shaked,et al.  Stability and guaranteed cost control of uncertain discrete delay systems , 2005 .

[16]  Sreten B. Stojanovic,et al.  A Lyapunov-Krasovskii methodology for asymptotic stability of discrete time delay systems , 2007 .

[17]  Wassim M. Haddad,et al.  Memoryless H∞ Controllers for Discrete-Time Systems with Time Delay , 1998, Autom..

[18]  Mohamed Darouach,et al.  Observers for discrete-time systems with multiple delays , 2001, IEEE Trans. Autom. Control..

[19]  Iu M Repin.  Quadratic liapunov functionals for systems with delay , 1965 .

[20]  Erik I. Verriest,et al.  Stability and Control of Time-delay Systems , 1998 .

[21]  Mou Chen,et al.  Backstepping Control of Uncertain Time Delay Systems Based on Neural Network , 2007, ISNN.

[22]  Jean-Pierre Richard,et al.  Time-delay systems: an overview of some recent advances and open problems , 2003, Autom..

[23]  Karl Johan Åström,et al.  Computer-Controlled Systems: Theory and Design , 1984 .

[24]  Ho-Chan Kim,et al.  Hinfinity control of discrete-time linear systems with time-varying delays in state , 1999, Autom..

[25]  Seong-Ho Song,et al.  H∞ control of discrete-time linear systems with time-varying delavs in state , 1999 .

[26]  M. Boutayeb,et al.  State feedback stabilization of discrete-time nonlinear systems , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..