Brief paper: On analytic and algebraic observability of nonlinear delay systems

Authors:
Milena Anguelova;Bernt Wennberg
Affiliations:
Mathematical Sciences, Chalmers University of Technology, SE-412 96 Gothenburg, Sweden and Mathematical Sciences, University of Gothenburg, SE-412 96 Gothenburg, Sweden;Mathematical Sciences, Chalmers University of Technology, SE-412 96 Gothenburg, Sweden and Mathematical Sciences, University of Gothenburg, SE-412 96 Gothenburg, Sweden
Venue:
Automatica (Journal of IFAC)
Year:
2010

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Abstract

The observability of nonlinear delay systems has previously been defined in an algebraic setting by a rank condition on modules over noncommutative rings. We introduce an analytic definition of observability to ensure the local uniqueness of state and initial conditions that correspond to a given input-output behaviour. It is shown that an algebraically observable delay system can be reformulated as a system of ordinary differential equations. Analytic observability is then decided by the local uniqueness of solutions to a boundary value problem for this ODE system.