Input-Output Finite-Time Stability of Discrete-Time Impulsive Switched Linear Systems with State Delays

This paper is concerned with the problem of input-output finite-time stability (IO-FTS) for discrete impulsive switched systems with state delays. Sufficient conditions are presented for the existence of IO-FTS for such systems under the cases of certain switching, arbitrary switching, and uncertain switching. All the obtained results are formulated in a set of linear matrix inequalities (LMIs). Two numerical examples are given to illustrate the effectiveness of the proposed results.

[1]  Francesco Amato,et al.  Input-output finite-time stability of linear systems , 2009, 2009 17th Mediterranean Conference on Control and Automation.

[2]  Hui Zhang,et al.  Robust energy-to-peak filtering for networked systems with time-varying delays and randomly missing data , 2010 .

[3]  Y. ORLOV,et al.  Finite Time Stability and Robust Control Synthesis of Uncertain Switched Systems , 2004, SIAM J. Control. Optim..

[4]  G. De Tommasi,et al.  Input-output finite-time stability of switching systems with uncertainties on the resetting times , 2011, 2011 19th Mediterranean Conference on Control & Automation (MED).

[5]  Francesco Amato,et al.  Finite-time control of linear systems subject to parametric uncertainties and disturbances , 2001, Autom..

[6]  Francesco Amato,et al.  Input-output finite time stabilization of linear systems , 2010, Autom..

[7]  Francesco Amato,et al.  Finite-Time Stability of Linear Time-Varying Systems: Analysis and Controller Design , 2010, IEEE Transactions on Automatic Control.

[8]  Francesco Amato,et al.  Input-Output Finite-Time Stability , 2011, ArXiv.

[9]  Hui Zhang,et al.  Robust ℋ︁∞ PID control for multivariable networked control systems with disturbance/noise attenuation , 2012 .

[10]  Francesco Amato,et al.  Input-output finite-time stabilization for a class of hybrid systems , 2010 .

[11]  Hui Zhang,et al.  Robust Static Output Feedback Control and Remote PID Design for Networked Motor Systems , 2011, IEEE Transactions on Industrial Electronics.

[12]  Gianmaria De Tommasi,et al.  Sufficient Conditions for Finite-Time Stability of Impulsive Dynamical Systems , 2009, IEEE Transactions on Automatic Control.

[13]  Francesco Amato,et al.  Finite-time stabilization of impulsive dynamical linear systems , 2011 .

[14]  Francesco Amato,et al.  Input–output finite-time stabilisation of a class of hybrid systems via static output feedback , 2011, Int. J. Control.

[15]  Sophie Tarbouriech,et al.  Finite-Time Stabilization of Linear Time-Varying Continuous Systems , 2009, IEEE Transactions on Automatic Control.

[16]  Shihua Li,et al.  Finite-time boundedness and L2-gain analysis for switched delay systems with norm-bounded disturbance , 2011, Appl. Math. Comput..

[17]  Shen Cong,et al.  Stability and output feedback stabilization for systems with Markovian switching and impulse effects , 2010 .

[18]  J.-T. Lim,et al.  Stability analysis of switched systems with impulse effects , 1999, Proceedings of the 1999 IEEE International Symposium on Intelligent Control Intelligent Systems and Semiotics (Cat. No.99CH37014).

[19]  Hui Zhang,et al.  H∞ Step Tracking Control for Networked Discrete-Time Nonlinear Systems With Integral and Predictive Actions , 2013, IEEE Transactions on Industrial Informatics.

[20]  Wei Zhu.  Stability analysis of switched impulsive systems with time delays , 2010 .

[21]  Yubin Liu,et al.  Razumikhin-Lyapunov functional method for the stability of impulsive switched systems with time delay , 2009, Math. Comput. Model..

[22]  K. Teo,et al.  A LMI approach to stability analysis and synthesis of impulsive switched systems with time delays , 2008 .

[23]  Xuemin Shen,et al.  On hybrid impulsive and switching systems and application to nonlinear control , 2005, IEEE Transactions on Automatic Control.

[24]  Shengyuan Xu,et al.  Robust H∞ stabilization for uncertain switched impulsive control systems with state delay: An LMI approach , 2008 .

[25]  Li Liu,et al.  Finite-time stability of linear time-varying singular systems with impulsive effects , 2008, Int. J. Control.

[26]  Jian Xiao,et al.  H∞ finite-time control for switched nonlinear discrete-time systems with norm-bounded disturbance , 2011, J. Frankl. Inst..

[27]  Hui Zhang,et al.  Robust weighted H∞ filtering for networked systems with intermittent measurements of multiple sensors , 2011 .

[28]  Francesco Amato,et al.  Input to Output Finite-Time Stabilization of Discrete-Time Linear Systems , 2011 .

[29]  Horacio J. Marquez,et al.  Controllability and Observability for a Class of Controlled Switching Impulsive Systems , 2008, IEEE Transactions on Automatic Control.

[30]  van der Arjan Schaft,et al.  50th IEEE Conference on Decision and Control and European Control Conference, 2011 , 2011 .

[31]  Yingmin Jia,et al.  Input-output finite-time stability and stabilization of stochastic Markovian jump systems , 2011, IEEE Conference on Decision and Control and European Control Conference.

[32]  Lin Sun,et al.  Input-output finite-time stability of time-varying linear singular systems , 2011, Proceedings of the 30th Chinese Control Conference.

[33]  A. Michel,et al.  Stability analysis of systems with impulse effects , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

[34]  Chao Liu,et al.  Robust L∞ reliable control for impulsive switched nonlinear systems with state delay , 2013 .

[35]  P. Dorato.  SHORT-TIME STABILITY IN LINEAR TIME-VARYING SYSTEMS , 1961 .