Random stabilization of sampled-data control systems with nonuniform sampling

For a sampled-data control system with nonuniform sampling, the sampling interval sequence, which is continuously distributed in a given interval, is described as a multiple independent and identically distributed (i.i.d.) process. With this process, the closed-loop system is transformed into an asynchronous dynamical impulsive model with input delays. Sufficient conditions for the closed-loop mean-square exponential stability are presented in terms of linear matrix inequalities (LMIs), in which the relation between the nonuniform sampling and the mean-square exponential stability of the closed-loop system is explicitly established. Based on the stability conditions, the controller design method is given, which is further formulated as a convex optimization problem with LMI constraints. Numerical examples and experiment results are given to show the effectiveness and the advantages of the theoretical results.

[1]  Guo-Ping Liu,et al.  Improvement of State Feedback Controller Design for Networked Control Systems , 2008, IEEE Transactions on Circuits and Systems II: Express Briefs.

[2]  Dong Yue,et al.  STATE FEEDBACK CONTROLLER DESIGN OF NETWORKED CONTROL SYSTEMS WITH PARAMETER UNCERTAINTY AND STATE‐DELAY , 2006 .

[3]  James Lam,et al.  Stabilization of linear systems over networks with bounded packet loss , 2007, Autom..

[4]  João Pedro Hespanha,et al.  Exponential stability of impulsive systems with application to uncertain sampled-data systems , 2008, Syst. Control. Lett..

[5]  Wei Zhang,et al.  Stability of networked control systems , 2001 .

[6]  Emilia Fridman,et al.  A refined input delay approach to sampled-data control , 2010, Autom..

[7]  Wen-an Zhang,et al.  Output Feedback Stabilization of Networked Control Systems With Packet Dropouts , 2007, IEEE Transactions on Automatic Control.

[8]  Long Wang,et al.  Stabilization of Networked Control Systems with Data Packet Dropout and Transmission Delays: Continuous-Time Case , 2005, Eur. J. Control.

[9]  Qing-Long Han,et al.  A New $H_{{\bm \infty}}$ Stabilization Criterion for Networked Control Systems , 2008, IEEE Transactions on Automatic Control.

[10]  Bo Wang,et al.  $H_{\infty}$ Controller Design for Networked Predictive Control Systems Based on the Average Dwell-Time Approach , 2010, IEEE Transactions on Circuits and Systems II: Express Briefs.

[11]  Hisaya Fujioka,et al.  Stability and stabilization of aperiodic sampled-data control systems using robust linear matrix inequalities , 2010, Autom..

[12]  Leonid Mirkin,et al.  Some Remarks on the Use of Time-Varying Delay to Model Sample-and-Hold Circuits , 2007, IEEE Transactions on Automatic Control.

[13]  Björn Wittenmark,et al.  Stochastic Analysis and Control of Real-time Systems with Random Time Delays , 1999 .

[14]  Hisaya Fujioka,et al.  A Discrete-Time Approach to Stability Analysis of Systems With Aperiodic Sample-and-Hold Devices , 2009, IEEE Transactions on Automatic Control.

[15]  Emilia Fridman,et al.  Robust sampled-data stabilization of linear systems: an input delay approach , 2004, Autom..

[16]  Dehui Sun,et al.  Fault tolerant control for networked control systems with packet loss and time delay , 2011, Int. J. Autom. Comput..

[17]  James Lam,et al.  A linear matrix inequality (LMI) approach to robust H/sub 2/ sampled-data control for linear uncertain systems. , 2003, IEEE transactions on systems, man, and cybernetics. Part B, Cybernetics : a publication of the IEEE Systems, Man, and Cybernetics Society.

[18]  Xiao-Ming Tang,et al.  Design of networked control systems with bounded arbitrary time delays , 2012, International Journal of Automation and Computing.

[19]  James Lam,et al.  A new delay system approach to network-based control , 2008, Autom..

[20]  Hisaya Fujioka.  Stability analysis of systems with aperiodic sample-and-hold devices , 2009, Autom..

[21]  Bruce A. Francis,et al.  Optimal Sampled-Data Control Systems , 1996, Communications and Control Engineering Series.

[22]  Young Soo Suh.  Stability and stabilization of nonuniform sampling systems , 2008, Autom..