Wirtinger's inequality and Lyapunov-based sampled-data stabilization

Discontinuous Lyapunov functionals appeared to be very efficient for sampled-data systems (Fridman, 2010; Naghshtabrizi, Hespanha, & Teel, 2008). In the present paper, new discontinuous Lyapunov functionals are introduced for sampled-data control in the presence of a constant input delay. The construction of these functionals is based on the vector extension of Wirtinger's inequality. These functionals lead to simplified and efficient stability conditions in terms of Linear Matrix Inequalities (LMIs). The new stability analysis is applied to sampled-data state-feedback stabilization and to a novel sampled-data static output-feedback problem, where the delayed measurements are used for stabilization.

[1]  ParkPooGyeon,et al.  Reciprocally convex approach to stability of systems with time-varying delays , 2011 .

[2]  E. Fridman,et al.  Networked‐based stabilization via discontinuous Lyapunov functionals , 2012 .

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

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

[5]  Kun Liu,et al.  Stability of linear systems with general sawtooth delay , 2010, IMA J. Math. Control. Inf..

[6]  Wim Michiels,et al.  Static output feedback stabilization: necessary conditions for multiple delay controllers , 2005, IEEE Transactions on Automatic Control.

[7]  Emilia Fridman,et al.  A new Lyapunov technique for robust control of systems with uncertain non-small delays , 2006, IMA J. Math. Control. Inf..

[8]  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.

[9]  PooGyeon Park,et al.  Reciprocally convex approach to stability of systems with time-varying delays , 2011, Autom..

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

[11]  K. Gu.  Discretized LMI set in the stability problem of linear uncertain time-delay systems , 1997 .

[12]  A. Teel,et al.  Stability of delay impulsive systems with application to networked control systems , 2007, 2007 American Control Conference.

[13]  E. Fridman,et al.  Exponential Stabilization of Delay Neutral Systems under Sampled-Data Control , 2005, Proceedings of the 2005 IEEE International Symposium on, Mediterrean Conference on Control and Automation Intelligent Control, 2005..

[14]  Sandro Zampieri,et al.  Trends in Networked Control Systems , 2008 .

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

[16]  Qing-Guo Wang,et al.  Delay-range-dependent stability for systems with time-varying delay , 2007, Autom..

[17]  PooGyeon Park,et al.  Stability and robust stability for systems with a time-varying delay , 2007, Autom..

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

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

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

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

[22]  Emilia Fridman,et al.  Descriptor discretized Lyapunov functional method: analysis and design , 2006, IEEE Transactions on Automatic Control.