Self-Triggered Real-Time Output Feedback Control Strategy For Stabilization of Passive and Output Feedback Passive Systems Technical Report of the ISIS Group at the University of Notre Dame isis-2010-002 October , 2010

In this paper, we propose a robust self-triggered real-time scheduling strategy for stabilization of passive or output feedback passive systems under unstruc tured uncertainties and in the presence of non-trivial actuation update delays. We assume that the u nstr ctured uncertainty is a L2 stable dynamic system in a feedback or feedforward interconnectio n with the model of the plant, we took the structure uncertainty into account to design the output feedback controller and we derived the selftriggered real-time scheduling strategy for both cases. St ability and expected inter-sampling time of the system under the proposed scheduling strategy is analyz ed in detail. Simulations are also provided to validate these results.

[1]  J. Willems.  Dissipative dynamical systems part I: General theory , 1972 .

[2]  Eduardo Sontag.  Smooth stabilization implies coprime factorization , 1989, IEEE Transactions on Automatic Control.

[3]  R. Freeman.  Global internal stabilizability does not imply global external stabilizability for small sensor disturbances , 1995, IEEE Trans. Autom. Control..

[4]  R. Freeman,et al.  Robust Nonlinear Control Design: State-Space and Lyapunov Techniques , 1996 .

[5]  Karl-Erik Årzén,et al.  A simple event-based PID controller , 1999 .

[6]  Zhong-Ping Jiang,et al.  Robust control of uncertain nonlinear systems via measurement feedback , 1999, IEEE Trans. Autom. Control..

[7]  Nicolas Chung Siong Fah,et al.  Input-to-state stability with respect to measurement disturbances for one-dimensional systems , 1999 .

[8]  K. Åström,et al.  Comparison of Riemann and Lebesgue sampling for first order stochastic systems , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[9]  James Moyne,et al.  Using deadbands to reduce communication in networked control systems , 2002, Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301).

[10]  Manel Velasco,et al.  The Self Triggered Task Model for Real-Time Control Systems , 2003 .

[11]  J.H. Braslavsky,et al.  Level Crossing Sampling in Feedback Stabilization under Data-Rate Constraints , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[12]  Paulo Tabuada,et al.  Event-Triggered Real-Time Scheduling of Stabilizing Control Tasks , 2007, IEEE Transactions on Automatic Control.

[13]  W. P. M. H. Heemels,et al.  Analysis of event-driven controllers for linear systems , 2008, Int. J. Control.

[14]  A. Anta,et al.  Self-triggered stabilization of homogeneous control systems , 2008, 2008 American Control Conference.

[15]  Xiaofeng Wang,et al.  Self-Triggered Feedback Control Systems With Finite-Gain ${\cal L}_{2}$ Stability , 2009, IEEE Transactions on Automatic Control.

[16]  Paulo Tabuada,et al.  To Sample or not to Sample: Self-Triggered Control for Nonlinear Systems , 2008, IEEE Transactions on Automatic Control.

[17]  Mrdjan J. Jankovic,et al.  Constructive Nonlinear Control , 2011 .