The inversion of a linear time-invariant time-delay system is considered. For such systems, a canonical form with isolated zero dynamics is obtained, system invariant zeros are investigated, and their relation to the spectral observability of the zero-dynamics subsystem is described. Based on these results, an inversion algorithm for time-delay systems is suggested.
The problem of transforming a controlled linear stationary system of differential equations with commensurable time delays into a canonical form with zero dynamics is considered. This problem has been well studied for ODE systems and is closely related to the concept of a relative degree. In this paper, the results are extended to time-delay systems.
We consider the problem of finding a bounded solution of a linear finite-difference equation with continuous time. We present conditions for the existence of such a solution and algorithms for finding the solution in real time under various additional assumptions.
An inversion problem for a linear time-invariant MIMO system with possibly unstable zero dynamics is considered. Sufficient conditions for the invertibility of such systems are given, and an algorithm for invertor synthesis is proposed. The results are extended to time-delay systems with commensurable delays.
Sufficient conditions for the invertibility of linear stationary dynamical systems are formulated. It is shown that the a priori information that the input signal is bounded substantially expands the class of systems for which the inversion problem is solvable.
We consider stationary linear vector systems with commensurable delays. We obtain sufficient conditions for the reducibility of such systems to canonical form with the extraction of null dynamics. A constructive algorithm for the reduction of a system to that form is presented. We suggest a method for estimating the unknown input for vector delay systems with given accuracy.
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