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 |