This paper develops sufficient conditions for the existence of global exponential observers for two classes of nonlinear systems: (i) the class of systems with a globally asymptotically stable compact set, and (ii) the class of systems that evolve on an open set. In the first class, the derived continuous-time observer also leads to the construction of a robust global sampled-data exponential o...

Proof. We denote V -[p] = { 1 , . . . , p}, A(G) is the set of acyclic orientations of G and a(G) = IA(G)I is their number. An n-coloring of G, c: V---> [n] induces an acyclic orientation DceA(G) as follows: If [x,y]eE is an edge, where c(x) > c(y) then in Dc this edge is oriented from x to y. Every acyclic orientation D ~ A(G) defines a partial order on V, which we denote by i>o. If D e A(G), ...

We introduce new methods for defining generalized sums of monotone operators and generalized compositions of monotone operators with linear maps. Under asymptotic conditions we show these operations coincide with the usual ones. When the monotone operators are subdifferentials of convex functions, a similar conclusion holds. We compare these generalized operations with previous constructions by...

This paper treats the antimaximum principle and the existence of a solution for quasilinear elliptic equation −div (a(x, |∇u|)∇u) = λm(x)|u|p−2u+ h(x) in Ω under the Neumann boundary condition. Here, a map a(x, |y|)y on Ω×RN is strictly monotone in the second variable and satisfies certain regularity conditions. This equation contains the p -Laplacian problem as a special case. Mathematics subj...

Over the last 20 years, many of the most spectacular results in the field of dynamical systems dealt specifically with interval and circle maps (or perturbations and complex extensions of such maps). Primarily, this is because in the one-dimensional case, much better distortion control can be obtained than for general dynamical systems. However, many of these spectacular results were obtained s...

The paper is a review of results on the asymptotic behavior of Markov processes generated by i.i.d. iterates of monotone maps. Of particular importance is the notion of splitting introduced by Dubins and Freedman (1966). Some extensions to more general frameworks are outlined, and, finally, a number of applications are indicated. *This paper is primarily based on my research with Professor Rabi...

Recent characterizations of various types of differentiable generalized monotone maps by Karamardian– Schaible–Crouzeix and their strengthened versions by Crouzeix–Ferland are extended to the nonsmooth case. For nondifferentiable locally Lipschitz maps necessary and/or sufficient conditions for quasimonotonicity, pseudomonotonicity and strict/ strong pseudomonotonicity are derived. To accomplis...

Making an extensive use of small transfinite topological dimension trind, we ascribe to every metric space X an ordinal number (or −1 or Ω) tHD(X), and we call it the transfinite Hausdorff dimension of X. This ordinal number shares many common features with Hausdorff dimension. It is monotone with respect to subspaces, it is invariant under bi-Lipschitz maps (but in general not under homeomorph...

Let f : (a, b)R. The function f is said to be matrix monotone if A ≤ B implies f(A) ≤ f(B) for all pairs of likesized self-adjoint matrices with spectrum in (a, b). Classically, Charles Loewner showed that a bounded Borel function is matrix monotone if and only if it is analytic and extends to be a self-map of the upper half plane. The theory of matrix montonicity has profound consequences for ...

We prove that every element of the polar cone to the closed convex cone of monotone transport maps can be represented as the divergence of a measure field taking values in the positive definite matrices.