This paper presents a design of dynamic feedback control based on observer for a class of large scale Lipschitz nonlinear systems. The use of Differential Mean Value Theorem (DMVT) is to introduce a general condition on the nonlinear functions. To ensure asymptotic stability, sufficient conditions are expressed in terms of linear matrix inequalities (LMIs). High performances are shown through r...

We present an operator space version of Rieffel’s theorem on the agreement of the metric topology, on a subset of the Banach space dual of a normed space, from a seminorm with the weak*-topology. As an application we obtain a necessary and sufficient condition for the matrix metric from an unbounded Fredholm module to give the BW-topology on the matrix state space of the C-algebra. Motivated by...

We consider a primal-dual potential reduction algorithm for nonlinear convex optimization problems over symmetric cones. The same comlexity estimates as in the case of the linear objective function are obtained provided a certain nonlinear system of equations can be solved with a given accuracy. This generalizes the result of K. Kortanek,F.Potra and Y.Ye [7]. We further introduce a generalized ...

Throughout this paper, the following conditions are assumed to hold. () n≥  is a positive integer, r ∈ C([t,∞),R+),  < a < b, τ > , σ > ; () p ∈ C([t,∞)× [a,b],R), q ∈ C([t,∞),R+), q ∈ C([t,∞),R+), h ∈ C([t,∞),R); () (u) is a continuously increasing real function with respect to u defined on R, and –(u) satisfies the local Lipschitz condition; () gi ∈ C(R,R), gi(u) satisfy the l...

Let M be a Lagrangian manifold, let the 1-form pdx be globally exact on M and let S(x, p) be defined by dS = pdx on M. Let H(x, p) be convex in p for all x and vanish on M . Let V (x) = inf{S(x, p) : p such that (x, p) ∈ M}. Recent work in the literature has shown that (i) V is a viscosity solution of H(x, ∂V/∂x) = 0 provided V is locally Lipschitz, and (ii) V is locally Lipschitz outside the s...

We introduce a notion of quasi regularity for points with respect to the inclusion F (x) ∈ C, where F is a nonlinear Fréchet differentiable function from Rv to Rm. When C is the set of minimum points of a convex real-valued function h on Rm and F ′ satisfies the L-average Lipschitz condition of Wang, we use the majorizing function technique to establish the semilocal linear/quadratic convergenc...