Stability of periodically time-varying systems: Periodic Lyapunov functions

Authors:
Christoph BöHm;Mircea Lazar;Frank AllgöWer
Affiliations:
Institute of Systems Theory and Automatic Control, University of Stuttgart, 70550 Stuttgart, Germany;Department of Electrical Engineering, Eindhoven University of Technology, 5612 AZ Eindhoven, The Netherlands;Institute of Systems Theory and Automatic Control, University of Stuttgart, 70550 Stuttgart, Germany
Venue:
Automatica (Journal of IFAC)
Year:
2012

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Abstract

This paper proposes a novel approach to stability analysis of discrete-time nonlinear periodically time-varying systems. The contributions are as follows. Firstly, a relaxation of standard Lyapunov conditions is derived. This leads to a less conservative Lyapunov function that is required to decrease at each period rather than at each time instant. Secondly, for linear periodic systems with constraints, it is shown that compared to standard Lyapunov theory, the novel concept of periodic Lyapunov functions allows for the calculation of a larger estimate of the region of attraction. An example illustrates the effectiveness of the developed theory.