This paper proposes an Lp (0<p<1) quasi norm state estimator for power system static estimation. Compared with the existing L, and L2 estimators, proposed can suppress bad data more effectively. The robustness of is discussed, analysis shows that its ability to increases as $p$ decreases. Moreover, algorithm suggested solve non-convex estimation pr...

A smooth curve γ : [0, 1] → S2 is locally convex if its geodesic curvature is positive at every point. J. A. Little showed that the space of all locally convex curves γ with γ(0) = γ(1) = e1 and γ (0) = γ(1) = e2 has three connected components L−1,c, L+1, L−1,n. The space L−1,c is known to be contractible. In this paper we prove that L+1 and L−1,n are homotopy equivalent to ΩS3 ∨ S2 ∨ S6 ∨ S10 ...

Previous results on Hessian measures by Trudinger and Wang are extended to the subelliptic case. Specifically we prove the weak continuity of the 2-Hessian operator, with respect to local L 1 convergence, for a system of m vector fields of step 2 and derive gradient estimates for the corresponding k-convex functions, 1 ≤ k ≤ m.

There exists a surface of a convex polyhedron P and a partition L of P into geodesic convex polygons such that there are no connected"edge"unfoldings of P without self-intersections (whose spanning tree is a subset of the edge skeleton of L).

If F is a vector space over an ordered division ring, C a convex subset of V and L the lattice of convex subsets of C, then we call L a convexity lattice. We give necessary and sufficient conditions for an abstract lattice to be a convexity lattice in the finite dimensional case.

Let Ω ⊂ R be a bounded open set. Given 2 ≤ m ≤ n, we construct a convex function φ : Ω → R whose gradient f = ∇φ is a Hölder continuous homeomorphism, f is the identity on ∂Ω, the derivative Df has rank m − 1 a.e. in Ω and Df is in the weak L space L. The proof is based on convex integration and staircase laminates.

Previous results on Hessian measures by Trudinger and Wang are extended to the subelliptic case. Specifically we prove the weak continuity of the 2-Hessian operator, with respect to local L 1 convergence, for a system of m vector fields of step 2 and derive gradient estimates for the corresponding k-convex functions, 1 ≤ k ≤ m.

This paper deals with the robust -control of discrete-time L# Markovian jump linear systems. It is assumed that both the state and jump variables are available to the controller. Uncertainties satisfying some norm bounded conditions are considered on the parameters of the system. An upperbound for the -control L# problem is derived in terms of an LMI optimization problem. For the case in which ...

Let L be the space of line transversals to a nite family of pairwise disjoint compact convex sets in R 3. We prove that each connected component of L can itself be represented as the space of transversals to some nite family of pairwise disjoint compact convex sets.

We consider a cross-layer optimization problem for multi-hop wireless networks over time varying channels. The system consists of L interfering links, where the transmission power and rate of link l (= 1, . . . , L) are specified in vectors ~ P = [P1 . . . PL] and ~ X = [X1 . . . XL] respectively. In every time slot, the scheduler schedules the transmissions by assigning a resource allocation v...