Decentralized Diagonal Dynamic Stabilization of Linear MultIvariable Systems

Abstract The diagonal stabilization problem (DSP) is defined over the ring of proper rational functions which have no poles inside a prescribed region of the finite complex plane. Solvability is intimately related to systems which exhibit the property of cyclicity. Necessary and sufficient conditions are established for the existence of solutions to the DSP. A complete parametrization of stabilizing controllers for the 2 × 2 case is given. Conditions of nonsolvability and hence nonstabilizability yield an explicit expression for the fixed modes of the system.

[1]  Nicos Karcanias,et al.  Structure, Smith-MacMillan form and coprime MFDs of a rational matrix inside a region P =ω∪{∞} , 1983 .

[2]  C. Desoer,et al.  The feedback interconnection of lumped linear time-invariant systems☆ , 1975 .

[3]  J. Murray,et al.  Feedback system design: The tracking and disturbance rejection problems , 1981 .

[4]  W. Wonham.  Linear Multivariable Control: A Geometric Approach , 1974 .

[5]  Nicos Karcanias,et al.  Proper and stable, minimal MacMillan degrees bases of rational vector spaces , 1984 .

[6]  D. Limebeer,et al.  Structure and Smith-MacMillan form of a rational matrix at infinity , 1982 .

[7]  W. Wolovich.  Linear multivariable systems , 1974 .

[8]  M. Vidyasagar,et al.  Algebraic and Topological Aspects of the Servo Problem for Lumped Linear Systems , 1981 .

[9]  C. Desoer,et al.  Feedback system design: The fractional representation approach to analysis and synthesis , 1979, 1979 18th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes.

[10]  N. Karcanias,et al.  Classification of proper bases of rational vector spaces: minimal MacMillian degree bases , 1983 .

[11]  Bruce A. Francis,et al.  Algebraic and topological aspects of the regulator problem for lumped linear systems , 1983, Autom..

[12]  M. Vidyasagar,et al.  Algebraic design techniques for reliable stabilization , 1982 .

[13]  Brian D. O. Anderson,et al.  Triangularization technique for the design of multivariable control systems , 1978 .

[14]  A. B. Özgüler,et al.  Diagonal stabilization of linear multivariable systems , 1986 .

[15]  A. Stephen Morse,et al.  Decentralized control of linear multivariable systems , 1976, Autom..

[16]  C. C. Macduffee,et al.  The Theory of Matrices , 1933 .

[17]  A. Morse.  System Invariants under Feedback and Cascade Control , 1976 .