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Time, Systems, and Control:Qualitative Properties and Methods

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Stability and Control of Dynamical Systems with Applications

Part of the book series: Control Engineering ((CONTRENGIN))

Abstract

This chapter presents some new results in the areas in which Professor Anthony N. Michel has been a world renowned researcher. Properties of time are summarized. These properties are linked to the features of physical variables expressed by the Physical Continuity and Uniqueness Principle and are important for modeling physical systems and for studies of their qualitative properties. The complete transfer function matrix is defined for multi-input multi-output time-invariant linear systems. This matrix is crucial for zero-pole cancellation, system minimal realization, and synthesis of stabilizing, tracking, and/or optimal control for the systems. A new Lyapunov methodology for nonlinear systems, called the “consistent Lyapunov methodology,” enables us to establish the necessary and sufficient conditions for (1) asymptotic stability, (2) direct construction of a Lyapunov function for a given nonlinear dynamical system, and (3) a set to be the exact domain of asymptotic stability. They are not expressed in terms of the existence of a Lyapunov function. The extended concepts of definite vector functions and of vector Lyapunov functions open new directions for studies of complex nonlinear dynamical systems and for their control synthesis.

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Authors
  1. Lyubomir T. Gruyitch
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Editors and Affiliations

  1. Department of Electrical and Computer Engineering, University of Illinois at Chicago, Chicago, Illinois, 60607, USA

    Derong Liu

  2. Department of Electrical Engineering, University of Notre Dame, Notre Dame, IN, 46556, USA

    Panos J. Antsaklis

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Gruyitch, L.T. (2003). Time, Systems, and Control:Qualitative Properties and Methods. In: Liu, D., Antsaklis, P.J. (eds) Stability and Control of Dynamical Systems with Applications. Control Engineering. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0037-6_2

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  • DOI: https://doi.org/10.1007/978-1-4612-0037-6_2

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-6583-2

  • Online ISBN: 978-1-4612-0037-6

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