Structual Approach to Instability and Chaos in Non-linear Causal Systems

The paper deals with structural properties of a class of strictly causal systems. It is shown that a special physically correct internal structure of a given system representation caled dissipation normal form can be derived as a natural consequence of strict causality, dissipativity, minimality and asymptotic stability requirements. A generalization of classic Tellegen’s theorem together with bi-orthonormal basis of the state velocity space expressing the signal energy conservation law for abstract system state space representations have been used. It is demonstrated by examples that the resulting structure represents a unifying tool for analysis and synthesis of a relatively general class of linear as well as nonlinear causal systems. Key-Words: energy-metric function, bi-orthonormal basis, dissipation normal form, Tellegen’s principle, non-linear phenomena, instability, chaotic behavior