A general approach for solving structurally constrained H ∞ suboptimal control problems is proposed. The structurally constrained problems include static output feedback control, decentralized control, and fixed controllers for different operating conditions. The approach uses a dual design formulation based on an H ∞ state-feedback controller parametrization result. The dual design condition i...

In this paper we prove a sharp affine Lp Sobolev inequality for functions on R. The new inequality is significantly stronger than (and directly implies) the classical sharp Lp Sobolev inequality of Aubin [A2] and Talenti [T], even though it uses only the vector space structure and standard Lebesgue measure on R. For the new inequality, no inner product, norm, or conformal structure is needed at...

A Bh set (or Sidon set of order h) in an Abelian group G is any subset {b0, b1, . . . , bn} ⊂ G with the property that all the sums bi1 + · · ·+ bih are different up to the order of the summands. Let φ(h, n) denote the order of the smallest Abelian group containing a Bh set of cardinality n+1. It is shown that, as h → ∞ and n is kept fixed, φ(h, n) ∼ 1 n! δl(△) h n , where δl(△ ) is the lattice...

Introduction Let P (x1, . . . , xn) be a homogeneous polynomial of degree d in n-real variables belonging to the class H described below. Let V (P ) = {x ∈ R/P (x) = 0} be the algebraic set that it defines. We prove the following inequality c1(P ).P − 2 d ≤ (−∆), c1(P ) > 0 in the operator sense on the domain C 0 (R n \ V (P )). This inequality while it is elementary to prove when the algebraic...

There are many important inequalities which are particular cases of Jensen’s inequality among which are the weighted A − G − H inequality, Cauchy’s inequality, the Ky Fan and Hölder’s inequalities. One can see that the lower bound zero is of global nature since it does not depend on p, x but only on f and the interval I whereupon f is convex. We give in 1 an upper global bound i.e., depending o...

and Applied Analysis 3 If b > h, from the second equation of model (6), one has: . v ≤ v (b − h − hmv) . (9) A standard comparison argument shows that lim sup t→∞ v (t) ≤ b − h hm ≜ α. (10) If b ≤ h, we have the following differential inequality: . v ≤ −hmv2 mv + 1 , (11) and the same argument above yields lim sup t→∞ v (t) ≤ 0. (12) In either case, the second inequality of (7) holds. 2.2. Boun...

This paper investigates an application of Neural Networks (NNs) to the decentralized guaranteed H∞ performance for a class of large-scale uncertain nonlinear systems. In order to guarantee the adequate H∞ performance level for the nonlinear systems, nonlinear linear matrix inequality (NLMI) condition is derived. The linear matrix inequality (LMI) approach instead of the NLMI is used to construc...

In this paper, we generalize Haagerup’s inequality [H] (on convolution norm in the free group) to a very general context of R-diagonal elements in a tracial von Neumann algebra; moreover, we show that in this “holomorphic” setting, the inequality is greatly improved from its originial form. We give an elementary combinatorial proof of a very special case of our main result, and then generalize ...