Global -exponential stabilisation of a class of nonlinear networked control systems

abstract In this paper, we investigate global -exponential stabilisation of a class of nonlinear networked control systems. The network-induced delays are assumed to be random and significantly smaller than the sampling period. First, sufficient conditions are presented to ensure global -exponential stability for a class of hybrid systems with time delay. Then, the networked control systems are modelled as the hybrid systems with time delay. By the techniques of adding a power integrator and a recursive argument, a sampled-data state feedback control law is presented. Sufficient conditions are given to ensure global -exponential stability of the closed-loop system by constructing a Lyapunov–Krasovskii function. Finally, a numerical example is presented to show the validity of the new methods.

[1]  Huijun Gao,et al.  Network-Based ${{\cal H}}_{\!\!\!\infty }$ Output Tracking Control , 2008, IEEE Transactions on Automatic Control.

[2]  Xu Hong.  Observer-based Sampled-data Control for a Class of Continuous Nonlinear Systems , 2010 .

[3]  Wei Lin,et al.  Non-Lipschitz continuous stabilizers for nonlinear systems with uncontrollable unstable linearization , 2001 .

[4]  Ji Li,et al.  Global finite-time stabilization by output feedback for planar systems without observable linearization , 2005, IEEE Transactions on Automatic Control.

[5]  George A. Perdikaris.  Computer Controlled Systems , 1991 .

[6]  Shihua Li,et al.  Global Robust Stabilization via Sampled‐Data Output Feedback for Nonlinear Systems with Uncertain Measurement and Control Gains , 2015 .

[7]  P. Kokotovic,et al.  Sufficient conditions for stabilization of sampled-data nonlinear systems via discrete-time approximations , 1999 .

[8]  Chunjiang Qian,et al.  Global Output Feedback Stabilization of a Class of Nonlinear Systems via Linear Sampled-Data Control , 2012, IEEE Transactions on Automatic Control.

[9]  Jie Chen,et al.  Extension of SGMF Using Gaussian Sum Approximation for Nonlinear/Non-Gaussian Model and Its Application in Multipath Estimation , 2013 .

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

[11]  Dragan Nesic,et al.  Explicit Computation of the Sampling Period in Emulation of Controllers for Nonlinear Sampled-Data Systems , 2009, IEEE Transactions on Automatic Control.

[12]  Hassan K. Khalil,et al.  Output feedback sampled-data control of nonlinear systems using high-gain observers , 2001, IEEE Trans. Autom. Control..

[13]  Wei Lin,et al.  A continuous feedback approach to global strong stabilization of nonlinear systems , 2001, IEEE Trans. Autom. Control..

[14]  I. Kolmanovsky,et al.  Nonsmooth stabilization of an underactuated unstable two degrees of freedom mechanical system , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

[15]  Iasson Karafyllis,et al.  Global stability results for systems under sampled-data control , 2007, 2007 European Control Conference (ECC).

[16]  Wei Chen,et al.  Network-based H∞ output tracking control for systems with time-varying bounded delay , 2011, Proceedings 2011 International Conference on Transportation, Mechanical, and Electrical Engineering (TMEE).

[17]  Iasson Karafyllis,et al.  Nonlinear Stabilization Under Sampled and Delayed Measurements, and With Inputs Subject to Delay and Zero-Order Hold , 2012, IEEE Transactions on Automatic Control.

[18]  Eduardo D. Sontag,et al.  FEEDBACK STABILIZATION OF NONLINEAR SYSTEMS , 1990 .

[19]  Zidong Wang,et al.  On global exponential stability of generalized stochastic neural networks with mixed time-delays , 2006, Neurocomputing.

[20]  Shihua Li,et al.  Global Stabilization of a Class of Inherently Nonlinear Systems under Sampled-data Control , 2014 .

[21]  L. Rosier.  Homogeneous Lyapunov function for homogeneous continuous vector field , 1992 .

[22]  Panos J. Antsaklis,et al.  Guest Editorial Special Issue on Networked Control Systems , 2004, IEEE Trans. Autom. Control..

[23]  Shihua Li,et al.  Semi-Global Stabilization Via Linear Sampled-Data Output Feedback for a Class of Uncertain Nonlinear Systems , 2013, ICONS.

[24]  Rafal Goebel,et al.  Solutions to hybrid inclusions via set and graphical convergence with stability theory applications , 2006, Autom..

[25]  L. Grüne.  Homogeneous state feedback stabilization of homogeneous systems , 2000, CDC.

[26]  Wei Lin,et al.  Nonsmooth output feedback stabilization of a class of genuinely nonlinear systems in the plane , 2003, IEEE Trans. Autom. Control..

[27]  Yiguang Hong,et al.  Finite-time stabilization and stabilizability of a class of controllable systems , 2002, Syst. Control. Lett..

[28]  Hassan K. Khalil,et al.  Performance recovery under output feedback sampled-data stabilization of a class of nonlinear systems , 2004, IEEE Transactions on Automatic Control.

[29]  Jian ZHANG,et al.  Observer-based Sampled-data Control for a Class of Continuous Nonlinear Systems: Observer-based Sampled-data Control for a Class of Continuous Nonlinear Systems , 2011 .

[30]  Nathan van de Wouw,et al.  Networked Control Systems With Communication Constraints: Tradeoffs Between Transmission Intervals, Delays and Performance , 2010, IEEE Transactions on Automatic Control.

[31]  M. Kawski.  Homogeneous Stabilizing Feedback Laws , 1990 .