About The variable Causality Dynamical Systems

Abstract

This paper deals with dynamical systems which models physical objects whose causal input-output ordering is changing during their evolution. Such a system is named Variable Causality Dynamical System (VCDS). VCDS are controlled from outside by a new input called causal ordering signal sharing the same set of state variables. In VCDS, all the variables, except the causal ordering signal, are gathered in two forms of so called global variables as current global variable and desired global variable. In this paper, different approaches of the causality concept are analyzed and there are proposed formal definitions for covariance and causality properties of variables and relations irrespective of the time domain. Two examples of VCDS are
presented here, one is described by a nonlinear algebraic existence relation and the other by a proper linear differential equation.