There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

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Convex Analysisの二,三の進展について

to be done in this area. Face recognition is a problem that scarcely clamoured for attention before the computer age but, having surfaced, has involved a wide range of techniques and has attracted the attention of some fine minds (David Mumford was a Fields Medallist in 1974). This singular application of mathematical modelling to a messy applied problem of obvious utility and importance but with no unique solution is a pretty one to share with students: perhaps, returning to the source of our opening quotation, we may invert Duncan's earlier observation, 'There is an art to find the mind's construction in the face!'.

Linear and nonlinear waves, by G. B. Whitham. Pp.636. £50. 1999. ISBN 0 471 35942 4 (Wiley).

关于Semigroups of Linear Operators and Applications to Partial Differential Equations的两个注解

Differential-Difference Equations. By Richard Bellman and Kenneth L. Cooke. Pp. xvi, 465. 1963. (Academic Press)

This paper presents a criterion to characterize control invariant polytopes for differential inclusion systems. The practice-oriented method, based on viability theory and convex analysis, can be applied to determine computational procedures to obtain families of control invariant polytopes. The criterion is based on a necessary and sufficient condition for viability to hold at any point on the boundary of a polytope.

/pdf/polytopic-control-invariant-sets-for-differential-inclusion-3nn0yheuqc.pdf

Polytopic control invariant sets for differential inclusion systems: A viability theory approach

https://hal.archives-ouvertes.fr/hal-01309675/document

Event-based stabilization of linear systems of conservation laws using a dynamic triggering condition

Boundary observers for linear and quasi-linear and quasi-linear hyperbolic systems with application to flow control

http://www.nt.ntnu.no/users/skoge/prost/proceedings/ifac2014/media/files/0404.pdf

State Estimation Based on Self-Triggered Measurements

This article deals with the design of saturated controls in the context of partial differential equations. It is focused on a linear Korteweg-de Vries equation, which is a mathematical model of waves on shallow water surfaces. In this article, we close the loop with a saturating input that renders the equation nonlinear. The well-posedness is proven thanks to the nonlinear semigroup theory. The proof of the asymptotic stability of the closed-loop system uses a Lyapunov function.

https://hal.archives-ouvertes.fr/hal-01193019/document

Christophe Prieur

Papers

Polytopic control invariant sets for differential inclusion systems: A viability theory approach

Event-based stabilization of linear systems of conservation laws using a dynamic triggering condition

Boundary observers for linear and quasi-linear and quasi-linear hyperbolic systems with application to flow control

State Estimation Based on Self-Triggered Measurements

Stabilization of a linear Korteweg-de Vries equation with a saturated internal control