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.
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.
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