document: Analysis of nonlinear time-delay systems using modules over non-commutative rings The theory of non-commutative rings is introduced to provide a basis for the study of nonlinear control systems with time delays . The left Ore ring of non-commutative polynomials defined over the field of a meromorphic function is suggested as the framework for such a study . This approach is then generalized to a broader class of nonlinear systems with delays that are called generalized Roesser systems . Finally , the theory is applied to analyze nonlinear time-delay systems . A weak observability is defined and characterized , generalizing the well-known linear result . Properties of closed submodules are then developed to obtain a result on the accessibility of such systems
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