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math.OC2019
A Generalization of the Passivity Theorem and the Small Gain Theorem Based on -Stability, with Application to a Parameter Adaptation Algorithm for Recursive Identification
Henri Bourlès
The usual passivity theorem considers a closed-loop, the direct chain of which consists of a strictly passive stable operator , and the feedback chain of which consists of a…
math.OC2015★ 1 cited
Algebraic Analysis Applied to the Theory of Linear Dynamical Systems
Henri Bourlès
The expression "Algebraic Analysis" was coined by Mikio Sato. It consists of using algebraic notions to solve analytic problem. The origin of Algebraic Analysis is Algebraic Geomet…
math.OC2011★ 1 cited
Injectivity and flatness of semitopological modules
Henri Bourlès
The spaces D, S and E' over \mathbb{R}^(n) are known to be flat modules over A=\mathbb{C}[\partial_{1},...,\partial_{n}], whereas their duals D', S' and E are known to be injective…