On arbitrary spectrum assignment in linear stationary systems with commensurate time delays in state variables by static output feedback

V. A. Zaitsev ; I. G. Kim

Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 27 (2017) no. 3, pp. 315-325

Résumé

We consider a control system defined by a linear time-invariant system of differential equations with commensurate delays in state \begin{equation} \dot x(t)=Ax(t)+\sum\limits_{j=1}^sA_jx(t-jh)+Bu(t),\quad y(t)=C^*x(t),\quad t>0. \tag{1} \end{equation} We construct a controller for the system $(1)$ as linear static output feedback $u(t)=\sum\limits_{\rho =0}^{\theta}Q_\rho y(t-\rho h)$. We study an arbitrary spectrum assignment problem for the closed-loop system. One needs to define a $\theta$ and to construct gain matrices $Q_{\rho}$, $\rho=0,\ldots,\theta$, such that the characteristic function of the closed-loop system with commensurate delays becomes a quasipolynomial with arbitrary preassigned coefficients. We obtain conditions on coefficients of the system $(1)$ under which the criterion is found for solvability of the problem of arbitrary spectrum assignment. Corollaries on stabilization by linear static output feedback with commensurate delays are obtained for the system $(1)$. An illustrative example is considered.

Détail

Keywords: linear delay systems, commensurate time delays, spectrum assignment problem, stabilization, static output feedback.

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