On State Realization and Causality Decomposition for Non-linear Systems
ROMANO M. DESANTIS · SIAM Journal on Control · 1973
While most of the research on the subject has either concentrated on the formulation and analysis of a state realization, or has dealt exclusively with causality decomposition, in this paper attention is focused on the interconnections between these two types of studies. More specifically, the following basic questions are considered : Does the knowledge of the causality structure of a system supply any information about the system state structure? Can the state structure tell something about the causality structure? The proposed answer can in part be summarized as follows. If a system is represented by the sum of strongly causal, strongly anticausal, memoryless, and strongly crosscausal parts, then strongly anticausal and memoryless components have nothing to do with a state realization of the system. On the other hand, any state realization of the system defines uniquely its strongly causal and strongly crosscausal parts. These and other relevant results are stated in quite a general context. They are applicable, for example, to systems which can be time-invariant or time-variant, linear or nonlinear, discrete-time or continuous-time or hybrid, finite state or infinite state.