Philippe Jouan

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The paper is concerned with asymptotic stability properties of linear switched systems. Under the hypothesis that all the subsystems share a non strict quadratic Lyapunov function, we provide a large class of switching signals for which a large class of switched systems are asymptotically stable. For this purpose we define what we call non chaotic inputs,(More)
In anterior pituitaries from male rats, it appeared that 5 alpha-androstane-3 beta,17 beta-diol was quickly metabolized into 5 alpha-androstane-3 beta,6 alpha-17 beta-triol and 5 alpha-androstane-3 beta,7 alpha,17 beta-triol by action of 6 alpha- and 7 alpha-hydroxylases. Hydroxysteroid hydroxylases were located in endoplasmic reticulum and were dependent(More)
In the male rat pituitary, 5alpha-androstane-3beta, 17beta-diol (3beta-diol) is extensively metabolized into polar steroids. They were identified as 5alpha-androstane-3beta, 6alpha-17beta-triol (6alpha-triol) and 5alpha-androstane-3beta, 7alpha, 17beta-triol (7alpha-triol). 6-alpha-Triol represents 53% and 7alpha-Triol 28% of the total 3beta-diol(More)
The aim of this paper is to give sufficient conditions for a switched linear system defined by a pair of Hurwitz matrices that share a common but not strict quadratic Lyapunov function to be GUAS. We show that this property is equivalent to the uniform observ-ability on [0, +∞) of a bilinear system defined on a subspace whose dimension is in most cases much(More)
The in vivo and in vitro metabolism of (3H)-5alpha-androstane-3lapha,17beta-diol by the male rat anterior pituitary was studied. A rapid and intensive conversion of 5alpha-androstane-3alpha, 17beta-diol into 5alpha-dihydrotestosterone was demonstrated, since following a 30 min. incubation time, 73% of the recovered radioactivity were constituted by(More)
We study the asymptotic stability properties of nonlinear switched systems under the assumption of the existence of a common weak Lyapunov function. We consider the class of nonchaotic inputs, which generalize the different notions of inputs with dwell-time, and the class of general ones. For each of them we provide some sufficient conditions for asymptotic(More)