Using exponential time-varying gains for sampled-data stabilization and estimation

This paper provides exponential stability results for two system classes. The first class includes a family of nonlinear ODE systems while the second consists of semi-linear parabolic PDEs. A common feature of both classes is that the systems they include involve sampled-data states and a time-varying gain. Sufficient conditions ensuring global exponential stability are established in terms of Linear Matrix Inequalities (LMIs) derived on the basis of Lyapunov-Krasovskii functionals. The established stability results prove to be useful in designing exponentially convergent observers based on sampled-data measurements. It is shown throughout simulated examples from the literature that the introduction of time-varying gains is beneficial to the enlargement of sampling intervals while preserving the stability of the system.

[1]  Alfredo Germani,et al.  A Chain Observer for Nonlinear Systems with Multiple Time-Varying Measurement Delays , 2014, SIAM J. Control. Optim..

[2]  Emilia Fridman,et al.  New Lyapunov-Krasovskii functionals for stability of linear retarded and neutral type systems , 2001, Syst. Control. Lett..

[3]  Emilia Fridman,et al.  Robust sampled-data control of a class of semilinear parabolic systems , 2012, Autom..

[4]  Iasson Karafyllis,et al.  From continuous-time design to sampled-data design of nonlinear observers , 2008, 2008 47th IEEE Conference on Decision and Control.

[5]  Emilia Fridman,et al.  Introduction to Time-Delay Systems: Analysis and Control , 2014 .

[6]  Emilia Fridman,et al.  Network-based H∞ filtering of parabolic systems , 2014, Autom..

[7]  Iasson Karafyllis,et al.  From Continuous-Time Design to Sampled-Data Design of Observers , 2009, IEEE Transactions on Automatic Control.

[8]  Mohammed M'Saad,et al.  Continuous-Discrete Time Observer for a class of MIMO Nonlinear Systems , 2013 .

[9]  J. Gauthier,et al.  A simple observer for nonlinear systems applications to bioreactors , 1992 .

[10]  Chung-Yao Kao,et al.  On robust stability of aperiodic sampled-data systems - An integral quadratic constraint approach , 2014, 2014 American Control Conference.

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

[12]  Paulo Tabuada,et al.  An introduction to event-triggered and self-triggered control , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

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

[14]  Boško.  Backstepping control of chemical tubular reactors , 2002 .

[15]  Iasson Karafyllis,et al.  Stability and Stabilization of Nonlinear Systems , 2011 .

[16]  Emilia Fridman,et al.  A new approach to enlarging sampling intervals for sampled-data systems , 2015 .

[17]  Miroslav Krstic,et al.  Backstepping control of chemical tubular reactors , 2002 .