Stability Analysis of Sampled-Data Systems Using Sum of Squares

This technical brief proposes a new approach to stability analysis of linear systems with sampled-data inputs or channels. The method, based on a variation of the discrete-time Lyapunov approach, provides stability conditions using functional variables subject to convex constraints. These stability conditions can be solved using the sum of squares methodology with little or no conservatism in both the case of synchronous and asynchronous sampling. Numerical examples are included to show convergence.

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

[2]  Laurentiu Hetel,et al.  Robust stability and control of switched linear systems , 2008 .

[3]  Vladimir L. Kharitonov,et al.  Stability of Time-Delay Systems , 2003, Control Engineering.

[4]  Antonis Papachristodoulou,et al.  Positive Forms and Stability of Linear Time-Delay Systems , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[5]  Hisaya Fujioka,et al.  Stability and stabilization of aperiodic sampled-data control systems: An approach using robust linear matrix inequalities , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[6]  Wim Michiels,et al.  Using delays and time-varying gains to improve the static output feedback stabilizability of linear systems: a comparison , 2004, IMA J. Math. Control. Inf..

[7]  Jamal Daafouz,et al.  Stabilization of Arbitrary Switched Linear Systems With Unknown Time-Varying Delays , 2006, IEEE Transactions on Automatic Control.

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

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

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

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

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

[13]  Jos F. Sturm,et al.  A Matlab toolbox for optimization over symmetric cones , 1999 .

[14]  P. Parrilo.  Structured semidefinite programs and semialgebraic geometry methods in robustness and optimization , 2000 .

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

[16]  Yutaka Yamamoto,et al.  A function space approach to sampled data control systems and tracking problems , 1994, IEEE Trans. Autom. Control..

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

[18]  Emilia Fridman,et al.  Discontinuous Lyapunov functionals for linear systems withsawtooth delays , 2009 .

[19]  Pablo A. Parrilo,et al.  Introducing SOSTOOLS: a general purpose sum of squares programming solver , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[20]  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.

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

[22]  Yingwei Zhang,et al.  Stability of networked control system with quantization , 2009, 2009 Chinese Control and Decision Conference.

[23]  Alexandre Seuret.  Stability analysis for sampled-data systems with a time-varying period , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

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

[25]  Corentin Briat,et al.  Convergence and Equivalence Results for the Jensen's Inequality—Application to Time-Delay and Sampled-Data Systems , 2011, IEEE Transactions on Automatic Control.