Asymptotic stabilization via output feedback for nonlinear systems with delayed output

We propose a novel and simple design scheme of output feedback controller for a class of nonlinear systems with delayed output. The nonlinear systems considered here are more general than feedforward systems (upper triangular systems). By constructing an appropriate Lyapunov–Krasovskii functional (LKF) and solving linear matrix inequalities (LMIs), the delay-dependent controller making the closed-loop system globally asymptotically stable (GAS) is explicitly constructed. A simulation example is given to demonstrate the effectiveness of the proposed design procedure.

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

[2]  Shengyuan Xu,et al.  Robust H ∞ filtering for a class of non-linear systems with state delay and parameter uncertainty , 2002 .

[3]  Alfredo Germani,et al.  A new approach to state observation of nonlinear systems with delayed output , 2002, IEEE Trans. Autom. Control..

[4]  Ye Xudong,et al.  Brief Universal stabilization of feedforward nonlinear systems , 2003 .

[5]  Xudong Ye,et al.  Universal stabilization of feedforward nonlinear systems , 2003, Autom..

[6]  Wei Lin,et al.  Using small feedback to stabilize a wider class of feedforward systems 1 , 1999 .

[7]  N. Carothers.  INTRODUCTION TO INEQUALITIES , 2007 .

[8]  X. Zhang,et al.  Global stabilization of a class of time-delay nonlinear systems , 2005, Int. J. Syst. Sci..

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

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

[11]  Mrdjan Jankovic,et al.  Integrator forwarding: A new recursive nonlinear robust design , 1997, Autom..

[12]  Jong-Tae Lim,et al.  Global exponential stabilization of a class of nonlinear systems by output feedback , 2005, IEEE Trans. Autom. Control..

[13]  Wei Lin,et al.  Output feedback control of a class of nonlinear systems: a nonseparation principle paradigm , 2002, IEEE Trans. Autom. Control..

[14]  Leonid Mirkin,et al.  H∞ control of system with I/O delay: a review of some problem‐oriented methods , 2002 .

[15]  Sabine Mondié,et al.  Global asymptotic stabilization of feedforward systems with delay in the input , 2004, IEEE Transactions on Automatic Control.

[16]  C. D. Souza,et al.  Delay-dependent robust stability and stabilization of uncertain linear delay systems: a linear matrix inequality approach , 1997, IEEE Trans. Autom. Control..

[17]  Laurent Praly.  Asymptotic stabilization via output feedback for lower triangular systems with output dependent incremental rate , 2003, IEEE Trans. Autom. Control..