Causality Structure of Engineering Systems

Santis, Romano M. De

doi:10.21236/ad0752568

Cited by 14 publications

(2 citation statements)

References 19 publications

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“…Using Proposition 3, this is equivalent to showing that T O is bounded and that for T = T o the following equations hold (4) TP t = PtTPt (5) TP t = PtTPt (6) f dPTdP = O.…”

Section: ~-1mentioning

confidence: 99%

Causality for nonlinear systems in Hilbert spaces

Santis

1973

Math. Systems Theory

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This paper is about the causality structure of systems in Hilbert spaces. While treatments on the subjects are usually confined to systems which enjoy properties such as linearity, boundedness, or nonpredictive behavior, here, all these properties play no essential role. As a consequence, new and more general results are obtained. These results concern the concepts of causality, anticausality, and crosscausality, and give necessary and sufficient conditions to decompose a general system into the sum of causal, anticausal, and crosscausal components. Introduction. In a number of recent publications [1], [2], [14], [16], [17],[18] various important connections between causality-related structure properties such as predictivity and nonpredictivity, and other systems properties such as those which are usually associated to optimality, sensitivity, and stability, have been established. Making further progress in this area appears difficult, however, because while most of the research on causality is concerned with linear, time-invariant and nonpredictive systems, the systems of interest in optimal control, sensitivity and stability theory, do not necessarily satisfy any one of these assumptions. Thus, the desirability arises for a causality study where more general types of systems might be considered.The most notable efforts to develop a study of this type are due to Porter [13] and Saeks [15], who considered linear systems in Banach and Hilbert spaces. These systems are allowed, among other things, to have a predictive behavior, and, as a consequence, they can be characterized by a complex causality structure. The approach adopted by those two authors has been, then, to start by analyzing the properties of basic systems with a simple causality structure. Later, they have used the results of this analysis to clarify the causality structure of more complicated systems. In particular the systems considered as basic, are either causal or anticausall, and according to an interesting conjecture by *

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“…Using Proposition 3, this is equivalent to showing that T O is bounded and that for T = T o the following equations hold (4) TP t = PtTPt (5) TP t = PtTPt (6) f dPTdP = O.…”

Section: ~-1mentioning

confidence: 99%

Causality for nonlinear systems in Hilbert spaces

Santis

1973

Math. Systems Theory

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show abstract

“…Lemma 2 is, in fact, also true for zVl triangular (the proofs given in the literature [6], [7] for the bounded case generalize in the obvious manner), though we will not need that fact here. Indeed, this extension of the lemma leads to a perturbation theorem for the existence of solutions of generalized Volterra equations to the effect that (l -(K + L)) has a densely defined triangular inverse (which is bounded when L is bounded) if (/ -K) has a bounded triangular inverse and L is any strictly triangular perturbation.…”

mentioning

confidence: 92%