A special coordinate basis of multivariable linear systems- Finite and infinite zero structure

A special coordinate basis of multivariable linear systems is introduced here. Several fundamental properties of linear systems regarding controllability (stabilisability), observability (detectability), invariant zeros, decoupling zeros, infinite zero structure, effect of feedback on zero structure, squaring down, diagonal and triangular decoupling .... etc can be directly displayed in terms of the special coordinate basis. Moreover, connections between the special coordinate basis and the important invariant subspaces of geometric theory of linear systems are established.

[1]  E. Davison,et al.  Properties and calculation of transmission zeros of linear multivariable systems , 1974, Autom..

[2]  T. Kailath,et al.  Comments on ‘ On structural invariants and the root-loci of linear multivariable systems’ , 1979 .

[3]  David H. Owens,et al.  On structural invariants and the root-loci of linear multivariable systems , 1978 .

[4]  Ali Saberi,et al.  Special coordinate basis for multivariable linear systems—finite and infinite zero structure, squaring down and decoupling , 1987 .

[5]  Ali Saberi,et al.  Output feedback control with almost disturbance decoupling property: A singular perturbation approach , 1984, The 23rd IEEE Conference on Decision and Control.

[6]  N. Karcanias,et al.  Poles and zeros of linear multivariable systems : a survey of the algebraic, geometric and complex-variable theory , 1976 .

[7]  H. Rosenbrock.  Correspondence : Correction to ‘The zeros of a system’ , 1974 .

[8]  P. Sannuti,et al.  A singular perturbation canonical form of invertible systems: determination of multivariate root-loci , 1983 .

[9]  A. Morse.  Structural Invariants of Linear Multivariable Systems , 1973 .

[10]  Ali Feliachi.  Decentralized stabilization of interconnected systems , 1986 .

[11]  Hassan K. Khalil,et al.  DECENTRALIZED STABILIZATION OF INTERCONNECTED SYSTEMS USING OUTPUT FEEDBACK. , 1985 .

[12]  H. Rosenbrock.  The zeros of a system , 1973 .

[13]  A. Saberi,et al.  Cheap and singular controls for linear quadratic regulators , 1985 .

[14]  Peddapullaiah Sannuti,et al.  Direct singular perturbation analysis of high-gain and cheap control problems , 1983, Autom..

[15]  P. Moylan.  Stable inversion of linear systems , 1977 .

[16]  L. Silverman.  Inversion of multivariable linear systems , 1969 .