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Generalized control systems, boundary control systems, and delayed control systems

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Abstract

We investigate the relationships between the three classes of systems mentioned in the title: we show that systems with delays in control are a special instance of boundary control systems, and a boundary control system produces a generalized control system when projected onto its (unstable) eigenspaces. We use this observation to investigate the action of feedback on the dynamical behavior of systems with boundary controls. In particular, the well-known fact that spectral controllability is necessary and sufficient for a system with delays in control to be stabilizable is derived from a general rather than from anad hoc method.

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Authors and Affiliations

  1. Dipartimento di Matematica, Politecnico di Torino, Corso Duca delgi Abruzzi 24, 10129, Torino, Italy

    L. Pandolfi

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  1. L. Pandolfi
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This paper was written according to the programs of the GNAFA-CNR group, with the financial support of the Italian “Ministero della Pubblica Istruzione.”

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Pandolfi, L. Generalized control systems, boundary control systems, and delayed control systems. Math. Control Signal Systems 3, 165–181 (1990). https://doi.org/10.1007/BF02551366

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  • DOI: https://doi.org/10.1007/BF02551366

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