On the Yakubovich frequency theorem for linear non-autonomous control processes

Roberta Fabbri;  ; Russell Johnson; Carmen Núñez;  ;

doi:10.3934/dcds.2003.9.677

On the Yakubovich frequency theorem for linear non-autonomous control processes

Discrete and Continuous Dynamical Systems ◽

10.3934/dcds.2003.9.677 ◽

2003 ◽

Vol 9 (3) ◽

pp. 677-704 ◽

Cited By ~ 18

Author(s):

Roberta Fabbri ◽

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Russell Johnson ◽

Carmen Núñez ◽

◽

...

Keyword(s):

Autonomous Control ◽

Frequency Theorem ◽

Control Processes

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Stabilization of control processes in Hilbert spaces

Proceedings of the Royal Society of Edinburgh Section A Mathematics ◽

10.1017/s0308210500010581 ◽

1978 ◽

Vol 81 (3-4) ◽

pp. 247-258 ◽

Cited By ~ 7

Author(s):

L. Pandolfi

Keyword(s):

Riccati Equation ◽

Hilbert Spaces ◽

Bounded Solution ◽

Positive Definite ◽

Autonomous Control ◽

Stabilization Problem ◽

Control Processes

SynopsisIn this paper we study the stabilization problem for non autonomous control processes in Hilbert spaces. We prove that a stabilizing feedback exists if and only if an associated Riccati equation has a bounded solution which is symmetric and positive definite.An application to control processes with delays in control is presented.

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A Bird in the Hand Isn’t Good for Long

Experimental Psychology (formerly Zeitschrift für Experimentelle Psychologie) ◽

10.1027/1618-3169/a000385 ◽

2018 ◽

Vol 65 (1) ◽

pp. 23-31 ◽

Cited By ~ 2

Author(s):

Stefan Scherbaum ◽

Simon Frisch ◽

Maja Dshemuchadse

Keyword(s):

Decision Making ◽

Cognitive Control ◽

The Other ◽

Decision Task ◽

Short Term ◽

Additional Time ◽

Control Processes ◽

Folk Wisdom ◽

Study Participants ◽

Insight Into

Abstract. Folk wisdom tells us that additional time to make a decision helps us to refrain from the first impulse to take the bird in the hand. However, the question why the time to decide plays an important role is still unanswered. Here we distinguish two explanations, one based on a bias in value accumulation that has to be overcome with time, the other based on cognitive control processes that need time to set in. In an intertemporal decision task, we use mouse tracking to study participants’ responses to options’ values and delays which were presented sequentially. We find that the information about options’ delays does indeed lead to an immediate bias that is controlled afterwards, matching the prediction of control processes needed to counter initial impulses. Hence, by using a dynamic measure, we provide insight into the processes underlying short-term oriented choices in intertemporal decision making.

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