Physical correctness of systems, state space representations, minimality and dissipativity

  • Authors:

  • Josef Hrusak;Milan Stork;Daniel Mayer

  • Affiliations:

  • Department of Applied Electronics and Telecommunications, University of West Bohemia, Plzen, Czech Republic;Department of Applied Electronics and Telecommunications, University of West Bohemia, Plzen, Czech Republic;Theory of Electrical Engineering, University of West Bohemia, Plzen, Czech Republic

  • Venue:
  • ICS'09 Proceedings of the 13th WSEAS international conference on Systems
  • Year:
  • 2009

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Abstract

This paper deals with internal stability and related structural properties of a relatively broad class of finite dimensional strictly causal systems, which can be described in the state-space representation form. Dissipativity, instability, asymptotic stability as well as stability in the sense of Lyapunov are analyzed by a new approach based on an abstract state energy concept. The resulting energy metric function is induced by the output signal power and determines both, the structure of a proper system representation as well as the corresponding system state space topology. A special form of physically correct internal structure of an equivalent state space representation has been derived for both the continuous- and discrete-time signals as a natural consequence of strict causality, signal energy conservation, dissipativity and state minimality requirements. Several typical problems are solved in detail, and results of simulation examples are shown for illustration of fundamental ideas and basic attributes of the proposed method.