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Finite spectrum assignment and observer for multivariable systems with commensurate delays. (English) Zbl 0596.93009

This paper deals with control systems of the form \[ dx/dt=A(z)x(t)+B(z)u(t),\quad y(t)=C(z)x(t) \] where x(t), u(t), and g(t) are real vectors of dimension n, m, and r, respectively, and where z is the right shift (delay) operator \(zx(t)=x(t-h)\), \(h>0\). A(z), B(z), and C(z) are matrices with elements which are polynomials in z. The paper enlarges the class of finite spectrum assignable systems to include spectrally controllable multivariable systems with commensurate delays. If the system is spectrally controllable, there is a delayed feedback matrix such that the closed-loop system is spectrally controllable through a single input. A result is also given on spectrally observable systems.
Reviewer: K.Cooke

MSC:

93B05 Controllability
34K35 Control problems for functional-differential equations
93C35 Multivariable systems, multidimensional control systems
15A18 Eigenvalues, singular values, and eigenvectors
93B07 Observability
93B55 Pole and zero placement problems
93C05 Linear systems in control theory
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