PSEUDO-LINEAR ALGEBRA: A POWERFUL TOOL IN UNIFICATION OF THE STUDY OF NONLINEAR CONTROL SYSTEMS

摘要

This paper introduces methods of pseudo-linear algebra to unify the algebraic formalism of one-forms and the related polynomial approach for both continuous and discrete-time nonlinear control systems. Given approach covers also differene, q-shift and q-difference operators whereby this algebraic formalism is not only unified but also extended to wide class of nonlinear control systems. Also the notion of transfer function of nonlinear control system is defined and some basic properties are shown. Transfer function definiton is based on skew polynomial ring which can be embedded into its quotient field.