Kybernetika 50 no. 4, 473-490, 2014

State elimination for nonlinear neutral state-space systems

Miroslav Halás and Pavol BistákDOI: 10.14736/kyb-2014-4-0473


The problem of finding an input-output representation of a nonlinear state space system, usually referred to as the state elimination, plays an important role in certain control problems. Though, it has been shown that such a representation, at least locally, always exists for both the systems with and without delays, it might be a neutral input-output differential equation in the former case, even when one starts with a retarded system. In this paper the state elimination is therefore extended further to nonlinear neutral state-space systems, and it is shown that also in such a case an input-output representation, at least locally, always exists. In general, it represents a neutral system again. Computational aspects related to the state elimination problem are discussed as well.


neutral systems, nonlinear time-delay systems, input-output representation, linear algebraic methods, Gröbner bases


93C10, 34K40, 93B25


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