A Scalable Robust Stability Criterion for Systems With Heterogeneous LTI Components

A scalable robust stability criterion for interconnected systems with heterogeneous linear time-invariant components is presented in this paper. The criterion involves only the properties of individual components and the spectrum of the interconnection matrix, which can be verified with relatively low computational effort, and more importantly maintains scalability of the analysis. Our main result shows that if the components are single-input-single-output (SISO), then the criterion has an appealing graphical interpretation which resembles the classical Nyquist criterion.

[1]  Ulf T. Jönsson,et al.  Duality Bounds in Robustness Analysis, , 1997, Autom..

[2]  A. Rantzer,et al.  System analysis via integral quadratic constraints , 1997, IEEE Trans. Autom. Control..

[3]  Ulf Jönsson,et al.  A scalable robust stability criterion for systems with heterogeneous LTI components , 2009, ACC.

[4]  Glenn Vinnicombe,et al.  Scalable robustness for consensus protocols with heterogeneous dynamics , 2005 .

[5]  Glenn Vinnicombe,et al.  The S-hull approach to consensus , 2007, 2007 46th IEEE Conference on Decision and Control.

[6]  C. Desoer,et al.  Feedback Systems: Input-Output Properties , 1975 .

[7]  Glenn Vinnicombe,et al.  ON THE STABILITY OF NETWORKS OPERATING TCP-LIKE CONGESTION CONTROL , 2002 .

[8]  A. Gattami,et al.  A frequency domain condition for stability of interconnected MIMO systems , 2004, Proceedings of the 2004 American Control Conference.

[9]  Rayadurgam Srikant,et al.  The Mathematics of Internet Congestion Control , 2003 .

[10]  R. Saeks,et al.  The analysis of feedback systems , 1972 .

[11]  Richard M. Murray,et al.  INFORMATION FLOW AND COOPERATIVE CONTROL OF VEHICLE FORMATIONS , 2002 .

[12]  Anders Rantzer,et al.  Duality Bounds in Robustness Analysis , 1996 .

[13]  H. Fujioka,et al.  Low dimensional stability criteria for large-scale interconnected systems , 2007, 2007 European Control Conference (ECC).

[14]  Ulf T. Jönsson,et al.  A Popov criterion for networked systems , 2007, Syst. Control. Lett..

[15]  Hisaya Fujioka,et al.  Characterization of Robust Stability of a Class of Interconnected Systems , 2007, ACC.

[16]  Reza Olfati-Saber,et al.  Consensus and Cooperation in Networked Multi-Agent Systems , 2007, Proceedings of the IEEE.

[17]  Ruggero Carli,et al.  Communication constraints in the average consensus problem , 2008, Autom..

[18]  Glenn Vinnicombe,et al.  Scalable Decentralized Robust Stability Certificates for Networks of Interconnected Heterogeneous Dynamical Systems , 2006, IEEE Transactions on Automatic Control.

[19]  Glenn Vinnicombe,et al.  Scalable robust stability for nonsymmetric heterogeneous networks , 2007, Autom..

[20]  Fernando Paganini,et al.  Internet congestion control , 2002 .

[21]  Sigurd Skogestad,et al.  Control of symmetrically interconnected plants , 1994, Autom..

[22]  Eduardo D. Sontag,et al.  Diagonal stability of a class of cyclic systems and its connection with the secant criterion , 2006, Autom..