We study the construction of the maximal controlled invariant set of switched linear systems. We consider two cases, based on whether fast switches are allowed or not. For both cases, iterative algorithms are given to construct such sets.

We give a simple upper bound for the upper box dimension of a forward invariant set of a C1-diffeomorphism of R. This result can be extended to the class of C1-mappings with finite topological degree. We apply these results to provide estimates for the dimension of the Hénon attractor and Julia sets in two complex variables. AMS classification scheme number: 37C45

Many examples exist of one-dimensional systems that are topologically conjugate to the shift operator on Σ2 and are thus chaotic. Most of these examples which have invariant Cantor subsets, have Cantor subsets of measure zero. In this paper we outline the formulation of a C map on a closed interval that has an invariant Cantor subset of positive Lebesgue measure. We also survey techniques used ...

Tracking of regions and object boundaries in an image sequence is a well studied problem in image processing and computer vision. So far, numerous approaches tracking different features of the objects (contours, regions or points of interest) have been presented. Most of these approaches have problems with robustness. Typical reasons are noisy images, objects with identical features or partial ...

In this paper, based on a generalized Lyapunov function, a simple proof is given to improve the estimation of globally attractive and positive invariant set of the Lorenz system. In particular, a new estimation is derived for the variable x. On the globally attractive set, the Lorenz system satisfies Lipschitz condition, which is very useful in the study of chaos control and chaos synchronizati...

A compactification of the set of conditioned invariant subspaces of fixed dimension for an observable pair (C, A) is proposed. It contains the almost conditioned invariant subspaces of the same dimension. In certain cases the compactification is shown to be smooth and a complete geometric description is given in the case of a single output system.

We demonstrate that viewpoint-invariant representations can be obtained from images for a useful class of 3D smooth object. The representations are stable over viewpoint, and also discriminate between different objects in the same class. They are computed using only image information, from the symmetry set of the object's outline. Examples are given of the representations obtained from real per...

In the first part, we recall the axiomatic definition of the elementary morphological operators (dilations, erosions, anti–dilations and anti–erosions) and their characterization in the case of Boolean lattices. This characterization is used to derive the set operator decompositions from the general decompositions of operators between complete lattices. In the second part, we define the notions...

In this paper, the behavior of a continuous flow in the vicinity of a closed positively .invariant subset in a metric space is investigated. The main theorem in this part in some sense generalizes previous results concerning classification of the flow near a compact invariant set in a locally compact metric space which was described by Ura-Kimura (1960) and Bhatia (1969). By applying the obtain...

We use the method of the tensor product graph to construct rational (Yangian invariant) solutions of the Yang-Baxter equation in fundamental representations of cn and thence the full set of cn-invariant factorized S-matrices. February 1, 2008 Supported by a U.K. Science and Engineering Research Council studentship. Address from 1st August: RIMS, Kyoto Univ., Kyoto 606, Japan. Integrable quantum...