A note on finding extreme points in multivariate space
Computational Statistics & Data Analysis
An algorithm for automatic Delaunay triangulation of arbitrary planar domains
Advances in Engineering Software
Control of chaos and synchronization
Systems & Control Letters - Special issue: Control of chaos and synchronization
On self-synchronization and controlled synchronization
Systems & Control Letters - Special issue: Control of chaos and synchronization
Advances in linear matrix inequality methods in control: advances in design and control
Advances in linear matrix inequality methods in control: advances in design and control
Poly-quadratic stability and global chaos synchronization of discrete time hybrid systems
Mathematics and Computers in Simulation - Chaos synchronization and control
Mathematics and Computers in Simulation
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The main purpose of this paper is to state some sufficient conditions for global synchronization of chaotic maps. The synchronization is viewed as a state reconstruction problem which is tackled by polytopic observers. Unlike most standard observers, polytopic observers can account for a special property of chaotic dynamics. Indeed, it is shown that many chaotic maps can be described in a so-called convexified form, involving a time-varying parameter which depends on the chaotic state vector. Such a form makes it possible to incorporate knowledge on the structure of the compact set wherein the parameter lies. This set depends implicitly on the structure of the chaotic attractor. It is proved that the conservatism of the polyquadratic stability conditions for the state reconstruction, stated in a companion paper, can be reduced when the corresponding Linear Matrix Inequalities involve the vertices of the minimal convex hull of this set. Theoretical developments along with special emphasis on computational aspects are provided and illustrated in the context of adaptive synchronization.