Robustness of nonlinear systems with respect to delay and sampling of the controls

We consider continuous time nonlinear time varying systems that are globally asymptotically stabilizable by state feedbacks. We study the stability of these systems in closed loop with controls that are corrupted by both delay and sampling. We establish robustness results through a Lyapunov approach of a new type.

[1]  Pierdomenico Pepe,et al.  Input-to-State Stability of Time-Delay Systems: A Link With Exponential Stability , 2008, IEEE Transactions on Automatic Control.

[2]  Zhong-Ping Jiang,et al.  On the Liapunov-Krasovskii methodology for the ISS of systems described by coupled delay differential and difference equations , 2008, Autom..

[3]  P. Kokotovic,et al.  A note on input-to-state stability of sampled-data nonlinear systems , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

[4]  Frédéric Mazenc,et al.  Backstepping for Nonlinear Systems with Delay in the Input Revisited , 2011, SIAM J. Control. Optim..

[5]  Dorothée Normand-Cyrot,et al.  Stabilization of linear input delayed dynamics under sampling , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[6]  Iasson Karafyllis,et al.  Predictor-Based Output Feedback for Nonlinear Delay Systems , 2011, ArXiv.

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

[8]  Rafael Castro-Linares,et al.  Trajectory tracking for non-holonomic cars: A linear approach to controlled leader-follower formation , 2010, 49th IEEE Conference on Decision and Control (CDC).

[9]  Alessandro Astolfi,et al.  Sampled-Data Control of Nonlinear Systems , 2006 .

[10]  M. Malisoff,et al.  Constructions of Strict Lyapunov Functions , 2009 .

[11]  Dragan Nesic,et al.  Open- and Closed-Loop Dissipation Inequalities Under Sampling and Controller Emulation , 2002, Eur. J. Control.

[12]  Arjan van der Schaft,et al.  Sampled data systems passivity and discrete port-Hamiltonian systems , 2005, IEEE Transactions on Robotics.

[13]  Guido Herrmann,et al.  A new approach to discretization applied to a continuous, nonlinear, sliding-mode-like control using nonsmooth analysis , 2001 .

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

[15]  Zongli Lin,et al.  On Input-to-State Stability for Nonlinear Systems with Delayed Feedbacks , 2007, 2007 American Control Conference.

[16]  Miroslav Krstic,et al.  Compensation of Time-Varying Input and State Delays for Nonlinear Systems , 2012 .

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

[18]  Hiroshi Ito,et al.  Lyapunov Technique and Backstepping for Nonlinear Neutral Systems , 2013, IEEE Transactions on Automatic Control.

[19]  Salvatore Monaco,et al.  Sampled-Data Stabilization; A PBC Approach , 2011, IEEE Transactions on Automatic Control.

[20]  Michael Malisoff,et al.  Stabilization of a chemostat model with Haldane growth functions and a delay in the measurements , 2010, Autom..

[21]  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.

[22]  Nathan van de Wouw,et al.  Networked control systems with communication constraints: Tradeoffs between transmission intervals and delays , 2009, 2009 European Control Conference (ECC).

[23]  W. E. Dixon,et al.  Predictor-Based Compensation for Electromechanical Delay During Neuromuscular Electrical Stimulation , 2011, IEEE Transactions on Neural Systems and Rehabilitation Engineering.

[24]  Dorothée Normand-Cyrot,et al.  Reduction Model Approach for Linear Systems With Sampled Delayed Inputs , 2013, IEEE Transactions on Automatic Control.

[25]  Hiroshi Ito,et al.  New stability analysis technique and backstepping for neutral nonlinear systems , 2012, 2012 American Control Conference (ACC).

[26]  Iasson Karafyllis,et al.  Nonlinear Stabilization Under Sampled and Delayed Measurements, and With Inputs Subject to Delay and Zero-Order Hold , 2012, IEEE Transactions on Automatic Control.

[27]  Nathan van de Wouw,et al.  Networked Control Systems With Communication Constraints: Tradeoffs Between Transmission Intervals, Delays and Performance , 2010, IEEE Transactions on Automatic Control.

[28]  Alexandre Seuret,et al.  Improved stability analysis of networked control systems under asynchronous sampling and input delay , 2010 .

[29]  Iasson Karafyllis,et al.  Global Stabilization of Feedforward Systems Under Perturbations in Sampling Schedule , 2011, SIAM J. Control. Optim..

[30]  Zhong-Ping Jiang,et al.  Saturated stabilization and tracking of a nonholonomic mobile robot , 2001 .

[31]  Salvatore Monaco,et al.  Advanced tools for nonlinear sampled-data systems' analysis and control , 2007, 2007 European Control Conference (ECC).