Generalized InputOutput Equations and Nonlinear Realizability.pdf

Generalized Input/Output Equations and Nonlinear Realizability∗ Yuan Wang Mathematics Department, Florida Atlantic University, Boca Raton, FL 33431 (407)367-3317, E-mail: ywang@control.math.fau.edu Abstract This work studies various types of input/output representations for analytic input/output op- erators. It is shown that if an operator satisfies an integro-differential input/output equation or an integral one, then it is locally realizable by analytic state space systems. This gener- alizes the results previously obtained for differential input/output equations to integral and integro-differential equations. 1 Introduction In the previous work (Wang Sontag 1992a, Wang Sontag 1992b), it was shown that if an input/output operator satisfies a possibly high-order differential input/output equation, then it is locally realizable by an analytic state space system (a set of controlled first order equations). Besides its intrinsic mathematical interest, this result is relevant in identification theory, since high-order equations involving only observed variables can be in principle determined from experimental data. In practice, however, the signals of physical systems are often affected by noise, which ∗This research was supported in part by NSF Grants DMS-9108250 and DMS-9403924 Keywords: Generating series, local realization of input/output operators, input/output equations. 1 makes numerical identification, especially under high frequency noise, a very difficult task for differential input/output equations. It is in principle better to work with integrals of the data instead. Indeed, in linear systems identification practice, it is often the case that one prefilters measured signals prior