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1 results

  • 5 - State Equivalence, State Reduction

  • from Part I - Lectures on Basics with Examples
  • Patrick Dewilde, Technische Universität München, Klaus Diepold, Technische Universität München, Alle-Jan Van der Veen, Technische Universiteit Delft, The Netherlands
  • Book:
    Time-Variant and Quasi-separable Systems
    Published online:
    24 October 2024
    Print publication:
    31 October 2024, pp 73-86

  • Summary

    In this chapter, we consider the central issue of minimality of the state-space system representation, as well as equivalences of representations. The question introduces important new basic operators and spaces related to the state-space description. In our time-variant context, what we call the Hankel operator plays the central role, via a minimal composition (i.e., product), of a reachability operator and an observability operator. Corresponding results for LTI systems (a special case) follow readily from the LTV case. In a later starred section and for deeper insights, the theory is extended to infinitely indexed systems, but this entails some extra complications, which are not essential for the main, finite-dimensional treatment offered, and can be skipped by students only interested in finite-dimensional cases.