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Unsolved Problems in Mathematical Systems and Control Theory by Vincent D. Blondel, Alexandre Megretski

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Problem 6.2

The strong stabilization problem for

linear time-varying systems

Avraham Feintuch

Department of Mathematics

Ben-Gurion University of the Negev

Beer-Sheva

Israel

abie@math.bgu.ac.il

1 DESCRIPTION OF THE PROBLEM

17400

feedback system {L, C} with plant L and compensator C, and {L, C} is stable if it has a bounded causal inverse. L is stabilizable if there exists a causal linear system C (not necessarily stable) such that {L, C} is stable.

The analogue of the result of Youla et al. which characterizes all stabilizable linear systems and parametrizes all stabilizers was given by Dale and Smith [4]:

2 MOTIVATION AND HISTORY OF THE PROBLEM ...

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