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In this paper, the problem of an exponential stability for time-delay systems with interval time-varying delays and nonlinear perturbations is investigated. Based on the Lyapunov method, a new delay-dependent criterion for exponential stability is established in terms of LMI (linear matrix inequalities). Numerical examples are carried out to support the effectiveness of our results. [ABSTRACT FROM AUTHOR]

A robust reliable control with integral quadratic constraint (IQC) performance for a class of uncertain systems with state and input delays is considered in this paper. Two classes of failure situations for sensor or actuator are studied. In the first class, a delay-dependent criterion for time-delay systems without perturbations is proposed to design the reliable control with IQC performance. Next, a criterion for uncertain time-delay systems with parameter uncertainties is obtained via simple derivations. The linear matrix inequality (LMI) approach is used to design a robust reliable state feedback control with IQC performance. In the second class, a reliable control with IQC performance is also provided from he previous method. A numerical example is given to illustrate the effectiveness of the procedure. [ABSTRACT FROM AUTHOR]

This paper presents a perturbation approach for performing sensitivity analysis of mathematical programming problems. Contrary to standard methods, the active constraints are not assumed to remain active if the problem data are perturbed, nor the partial derivatives are assumed to exist. In other words, all the elements, variables, parameters, Karush-Kuhn-Tucker multipliers, and objective function values may vary provided that optimality is maintained and the general structure of a feasible perturbation (which is a polyhedral cone) is obtained. This allows determining: (a) the local sensitivities, (b) whether or not partial derivatives exist, and (c) if the directional derivative for a given direction exists. A method for the simultaneous obtention of the sensitivities of the objective function optimal value and the primal and dual variable values with respect to data is given. Three examples illustrate the concepts presented and the proposed methodology. Finally, some relevant conclusions are drawn. [ABSTRACT FROM AUTHOR]

We consider the proximal form of a bundle algorithm for minimizing a nonsmooth convex function, assuming that the function and subgradient values are evaluated approximately. We show how these approximations should be controlled in order to satisfy the desired optimality tolerance. For example, this is relevant in the context of Lagrangian relaxation, where obtaining exact information about the function and subgradient values involves solving exactly a certain optimization problem, which can be relatively costly (and as we show, in any case unnecessary). We show that approximation with some finite precision is sufficient in this setting and give an explicit characterization of this precision. Alternatively, our result can be viewed as a stability analysis of standard proximal bundle methods, as it answers the following question: for a given approximation error, what kind of approximate solution can be obtained and how does it depend on the magnitude of the perturbation? Key Words. Nonsmooth optimization; convex optimization; bundle methods; stability analysis; perturbations. [ABSTRACT FROM AUTHOR]