Stability of networked control systems with bounded sampling rates and time delays

In this paper we study stability properties of networked control systems whose control loops are subject to sampling rates and time delays, both time varying. We represent these time incertitudes as non-static parametric uncertainties in the linear discrete-time closed-loop model. Then we apply robust control techniques, and present a sufficient stability condition based on interval algebra methods that allows testing system stability by simply evaluating a time invariant matrix.

[1]  Ramon E. Moore Methods and applications of interval analysis , 1979, SIAM studies in applied mathematics.

[2]  G. Alefeld,et al.  Introduction to Interval Computation , 1983 .

[3]  Huang Lin,et al.  Root locations of an entire polytope of polynomials: It suffices to check the edges , 1987, 1987 American Control Conference.

[4]  B. Barmish,et al.  Polytopes of polynomials with zeros in a prescribed set , 1989 .

[5]  Pradeep Misra On Stabilization of Systems with Uncertain Parameters: An Interval Arithmetic Approach , 1989, 1989 American Control Conference.

[6]  Roberto Tempo,et al.  On the Nyquist Envelope of an Interval Plant Family , 1991, 1991 American Control Conference.

[7]  Roberto Tempo,et al.  Extreme point results for robust stabilization of interval plants with first-order compensators , 1992 .

[8]  Wang Lon EXTREME POINT RESULTS FOR STRICT POSITIVE REALNESS OF TRANSFER FUNCTION FAMILIES , 1994 .

[9]  Lin Huang,et al.  Vertex results for uncertain systems , 1994 .

[10]  Umit Ozguner,et al.  Stability of a set of matrices: a control theoretic approach , 1995, Proceedings of 1995 34th IEEE Conference on Decision and Control.

[11]  Johan Nilsson,et al.  Stochastic Analysis and Control of Real-Time Systems with Random Time Delays , 1996 .

[12]  Linda Bushnell,et al.  Stability analysis of networked control systems , 1999, Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251).

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

[14]  Bruce A. Francis,et al.  Stabilization with control networks , 2002, Autom..

[15]  Dong-Sung Kim,et al.  A scheduling method for network-based control systems , 2002, IEEE Trans. Control. Syst. Technol..

[16]  P. Marti,et al.  Control loop scheduling paradigm in distributed control systems , 2003, IECON'03. 29th Annual Conference of the IEEE Industrial Electronics Society (IEEE Cat. No.03CH37468).

[17]  Chung-Yao Kao,et al.  Simple stability criteria for systems with time-varying delays , 2004, Autom..

[18]  Robin J. Evans,et al.  Stabilizability of Stochastic Linear Systems with Finite Feedback Data Rates , 2004, SIAM J. Control. Optim..

[19]  Vicenç Puig,et al.  Simulation of uncertain dynamic systems described by interval models: A survey , 2005 .

[20]  Manel Velasco,et al.  Bandwidth Management for Distributed Control of Highly Articulated Robots , 2005, Proceedings of the 2005 IEEE International Conference on Robotics and Automation.

[21]  Pau Marti,et al.  A probabilistic approach to the stability analysis of real-time control systems , 2005 .

[22]  ASYMPTOTIC STABILITY OF AN EQUILIBRIUM P . OSITION OF A FAMILY OF SYSTEMS OF LINEAR DIFFERENTIAL EQUATIONS , 2022 .