Simultaneous finite- and infinite-zero assignments of linear systems

Abstract A simultaneous finite- and infinite-zero assignment problem via sensor selection for linear multivariable systems is proposed. By sensor selection we mean an appropriate choice of the output matrix C. Here, by utilizing the well-known Burnovsky canonical form for a linear system characterized by the matrix pair ( A , B ), we obtain an explicit construction algorithm that generates a non-empty set C of output matrices such that for any member C of this set, the corresponding system characterized by the triple ( A , B , C ) has the prescribed finite- and infinite-zero structures. Two examples are also given to illustrate our results.

[1]  Antonis I. G. Vardulakis,et al.  Zero placement and the ‘ squaring down ’ problem: a polynomial matrix approach , 1980 .

[2]  Ali Saberi,et al.  Explicit expressions for cascade factorization of general nonminimum phase systems , 1992 .

[3]  Y. Hung,et al.  On the relationships between unbounded asymptote behaviour of multivariable root loci, impulse response and infinite zeros , 1981, 1981 20th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes.

[4]  H. Rosenbrock,et al.  State-space and multivariable theory, , 1970 .

[5]  J. Dion,et al.  Structure at infinity of linear multivariable systems a geometric approach , 1981, 1981 20th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes.

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

[7]  Nicos Karcanias,et al.  Decentralized determinantal assignment problem: fixed and almost fixed modes and zeros , 1988 .

[8]  Frank L. Lewis,et al.  Transmission Zero Assignment using Semistate Descriptions , 1992, 1992 American Control Conference.

[9]  Paul Van Dooren,et al.  Computation of zeros of linear multivariable systems , 1980, Autom..

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

[11]  Vassilis L. Syrmos.  On the finite transmission zero assignment problem , 1993, Autom..

[12]  A. Pugh,et al.  On the zeros and poles of a rational matrix , 1979 .

[13]  Ali Saberi.  Decentralization of large-scale systems: A new canonical form for linear multivariable systems , 1985 .

[14]  Ali Saberi,et al.  Loop Transfer Recovery: Analysis and Design , 1993 .