Distributed control of positive systems

Stabilization and optimal control is studied for state space systems with nonnegative coefficients (positive systems). In particular, we show that a stabilizing distributed feedback controller, when it exists, can be computed using linear programming. The same methods are also used to minimize the closed loop input-output gain. An example devoted to distributed control of a vehicle platoon is examined.

[1]  Mustapha Ait Rami,et al.  Solvability of static output-feedback stabilization for LTI positive systems , 2011, Syst. Control. Lett..

[2]  Federico Najson,et al.  On the Kalman–Yakubovich–Popov lemma for discrete-time positive linear systems: a novel simple proof and some related results , 2013, Int. J. Control.

[3]  V. Blondel,et al.  The presence of a zero in an integer linear recurrent sequence is NP-hard to decide , 2002 .

[4]  Charles R. Johnson.  Review: Abraham Berman and Robert J. Plemmons,Nonnegative matrices in the mathematical sciences , 1982 .

[5]  David Angeli,et al.  Monotone control systems , 2003, IEEE Trans. Autom. Control..

[6]  Robert J. Plemmons,et al.  Nonnegative Matrices in the Mathematical Sciences , 1979, Classics in Applied Mathematics.

[7]  F. Tadeo,et al.  Controller Synthesis for Positive Linear Systems With Bounded Controls , 2007, IEEE Transactions on Circuits and Systems II: Express Briefs.

[8]  Javad Lavaei,et al.  Power flow optimization using positive quadratic programming , 2011 .

[9]  J. Lei.  Monotone Dynamical Systems , 2013 .

[10]  Jan C. Willems,et al.  Lyapunov functions for diagonally dominant systems , 1975, Autom..

[11]  F. Fairman.  Introduction to dynamic systems: Theory, models and applications , 1979, Proceedings of the IEEE.

[12]  Jean-Charles Delvenne,et al.  The continuous Skolem-Pisot problem , 2010, Theor. Comput. Sci..

[13]  Dirk Aeyels,et al.  Stabilization of positive linear systems , 2001, Syst. Control. Lett..

[14]  Takashi Tanaka,et al.  KYP lemma for internally positive systems and a tractable class of distributed H-infinity control problems , 2010, Proceedings of the 2010 American Control Conference.

[15]  L. Hörmander.  The analysis of linear partial differential operators , 1990 .

[16]  L. Moreau,et al.  Stability of continuous-time distributed consensus algorithms , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).