Observer-based output feedback control of sampled-data system under stochastic sampling

This paper is concerned with output feedback stabilization problem for a class of sampled-data systems under stochastic sampling. Different from the existing results, a systems matrix A whose eigenvalues contain zero is allowed. By combining the Kronecker product operation with the Vandermonde matrix, a sufficient condition is developed to guarantee the stochastic stability of the closed-loop system. Based on linear matrix inequality (LMI) and a cone complementarity linearization algorithm, a method of designing an observer-based output feedback controller for the system is given. Finally, a simulation example is given to show the effectiveness of the proposed method.

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

[2]  Alexandre Seuret,et al.  A novel stability analysis of linear systems under asynchronous samplings , 2012, Autom..

[3]  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.

[4]  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.

[5]  L. Ghaoui,et al.  A cone complementarity linearization algorithm for static output-feedback and related problems , 1997, IEEE Trans. Autom. Control..

[6]  João Pedro Hespanha,et al.  A Survey of Recent Results in Networked Control Systems , 2007, Proceedings of the IEEE.

[7]  William S. Levine,et al.  Handbook Of Networked And Embedded Control Systems , 2007 .

[8]  E. Fridman,et al.  Sampled-data H ∞ control and filtering : Nonuniform uncertain sampling , 2007 .

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

[10]  G. A. Medrano-Cersa.  Robust computer control of an inverted pendulum , 1999 .

[11]  Y. Shu.  Stability and stabilization of nonuniform sampling systems. , 2008 .

[12]  John Baillieul,et al.  Handbook of Networked and Embedded Control Systems , 2005, Handbook of Networked and Embedded Control Systems.

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

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

[15]  Huijun Gao,et al.  Robust sampled-data H∞ control with stochastic sampling , 2009, Autom..

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

[17]  Deqiang Gan,et al.  A method for evaluating the performance of PSS with saturated input , 2007 .

[18]  Cleve B. Moler,et al.  Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later , 1978, SIAM Rev..

[19]  Ya-Jun Pan,et al.  Output feedback stabilization for Markov-based nonuniformly sampled-data networked control systems , 2013, Syst. Control. Lett..

[20]  Hak-Keung Lam,et al.  Stabilization of Nonlinear Systems Using Sampled-Data Output-Feedback Fuzzy Controller Based on Polynomial-Fuzzy-Model-Based Control Approach , 2012, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[21]  J. Alvarez-Ramirez,et al.  Stability of single saturated-input linear systems with one zero eigenvalue , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[22]  Tingwen Huang,et al.  Stabilization for sampled-data systems under noisy sampling interval , 2016, Autom..

[23]  Emilia Fridman,et al.  Sampled-data Hinfinity control and filtering: Nonuniform uncertain sampling , 2007, Autom..

[24]  Gene F. Franklin,et al.  Digital Control Of Dynamic Systems 3rd Edition , 2014 .

[25]  Boris Tovornik,et al.  Swinging up and stabilization of a real inverted pendulum , 2006, IEEE Transactions on Industrial Electronics.

[26]  Gene F. Franklin,et al.  Digital control of dynamic systems , 1980 .

[27]  Luca Zaccarian,et al.  Output feedback synthesis for sampled-data system with input saturation , 2010, Proceedings of the 2010 American Control Conference.