Output feedback decentralized control of large-scale systems using weighted sensitivity functions minimization

This paper considers the problem of achieving stability and desired dynamical transient behavior for linear large-scale systems, by decentralized control. It can be done by making the effects of the interconnections between the subsystems arbitrarily small. Sufficient conditions for stability and diagonal dominance of the closed-loop system are introduced. These conditions are in terms of decentralized subsystems and directly make a constructive H∞ control design possible. A mixed H∞ pole region placement is suggested, such that by assigning the closed-loop eigenvalues of the isolated subsystems appropriately, the eigenvalues of the overall closed-loop system are assigned in desirable range. The designs are illustrated by an example.

[1]  Bruce A. Francis,et al.  Feedback Control Theory , 1992 .

[2]  Donald T. Gavel,et al.  Decentralized adaptive control: structural conditions for stability , 1989 .

[3]  M. Araki Stability of large-scale nonlinear systems--Quadratic-order theory of composite-system method using M-matrices , 1978 .

[4]  Alan J. Laub,et al.  The LMI control toolbox , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[5]  Osita D. I. Nwokah,et al.  Quantitative Feedback Design of Decentralized Control Systems , 1993 .

[6]  G. Zames Feedback and optimal sensitivity: Model reference transformations, multiplicative seminorms, and approximate inverses , 1981 .

[7]  Dragoslav D. Šiljak,et al.  Decentralized control and computations: status and prospects , 1996 .

[8]  E. Davison,et al.  On the stabilization of decentralized control systems , 1973 .

[9]  Boris Lohmann,et al.  Decentralized control via eigenstructure assignment , 2000, Smc 2000 conference proceedings. 2000 ieee international conference on systems, man and cybernetics. 'cybernetics evolving to systems, humans, organizations, and their complex interactions' (cat. no.0.

[10]  D. J. Hawkins 'Pseudodiagonalisation' and the inverse-Nyquist array method , 1972 .

[11]  A. Mees Achieving diagonal dominance , 1981 .

[12]  D. Siljak Stability of Large-Scale Systems , 1972 .

[13]  P. Peres,et al.  On a convex parameter space method for linear control design of uncertain systems , 1991 .

[14]  Jan Lunze,et al.  Feedback control of large-scale systems , 1992 .

[15]  M. Corless,et al.  Continuous state feedback guaranteeing uniform ultimate boundedness for uncertain dynamic systems , 1981 .

[16]  N. Munro Recent extensions to the inverse Nyquist array design method , 1985, 1985 24th IEEE Conference on Decision and Control.

[17]  Youxian Sun,et al.  Output feedback decentralized stabilization: ILMI approach , 1998 .

[18]  B. Francis,et al.  A Course in H Control Theory , 1987 .

[19]  Ali Khaki Sedigh,et al.  Sufficient condition for stability of decentralised control , 2000 .

[20]  A. Michel,et al.  Stability analysis of composite systems , 1972 .

[21]  Pascal Gahinet,et al.  H/sub /spl infin// design with pole placement constraints: an LMI approach , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[22]  F. N. Bailey,et al.  The Application of Lyapunov’s Second Method to Interconnected Systems , 1965 .

[23]  P. Gahinet,et al.  H∞ design with pole placement constraints: an LMI approach , 1996, IEEE Trans. Autom. Control..

[24]  M. Abrishamchian,et al.  Sufficient condition for stability of decentralized control feedback structures , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

[25]  Boris Lohmann,et al.  Decentralized stabilization using descriptor systems , 2000, Smc 2000 conference proceedings. 2000 ieee international conference on systems, man and cybernetics. 'cybernetics evolving to systems, humans, organizations, and their complex interactions' (cat. no.0.

[26]  L. F. Yeung,et al.  New dominance concepts for multivariable control systems design , 1992 .

[27]  R. Skelton,et al.  A complete solution to the general H∞ control problem: LMI existence conditions and state space formulas , 1993, 1993 American Control Conference.

[28]  Pascal Gahinet,et al.  Explicit controller formulas for LMI-based H∞ synthesis , 1996, Autom..

[29]  D. Siljak Large-Scale Systems: Complexity, Stability, Reliability , 1975 .

[30]  Si-Ying Zhang,et al.  Stability of linear large-scale composite systems , 1994, Proceedings of 1994 American Control Conference - ACC '94.

[31]  G. Stewart Introduction to matrix computations , 1973 .

[32]  Carl N. Nett,et al.  An Explicit Formula and an Optimal Weight for the 2-Block Structured Singular Value Interaction Measure , 1987, 1987 American Control Conference.

[33]  Manfred Morari,et al.  Interaction measures for systems under decentralized control , 1986, Autom..

[34]  B. Noble Applied Linear Algebra , 1969 .

[35]  Ian Postlethwaite,et al.  Multivariable Feedback Control: Analysis and Design , 1996 .