Volterra and Algebraic Approaches to the Zero Dynamics

Detta är en avhandling från Linköping : Linköping University

Sammanfattning: The zero dynamics is a property of affi.ne nonlinear systems w hich has been extensively studied during the last decade. Its properties are important in several contexts such as exact linearization, stabilization and sliding mode control. We will first give a result which considers how zeros of the sequence of transfer functions that emerge from the Laplace transform of the regular kernels in a Volterra series are connected to the zero dynamics. It is shown that if a certain factorization can be performed then zeros in the right half plane gives an unstable zero dynamics. This can be viewed as a generalization of the linear case.Further, a result is given which shows how differential algebra, in particular the Ritt algorithm, can be used to calculate zero dynamics. For a large dass of affi.ne SISO state space descriptions the Ritt algorithm, with a certain ranking, is shown to give the zero dynamics. This indicates that the concept of zero dynamics can be generalized to more complex state space descriptions.

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