Uncertain delay differential equation is a type of functional differential equations driven by canonical process. This paper presents a method to solve an uncertain delay differential equation, and proves an existence and uniqueness theorem of solution for uncertain delay differential equations under Lipschitz condition and linear growth condition by Banach fixed point theorem.

although the corrupted condition is not protected by sanctions, there are three beliefs as to whether its corruption (fasād) permeates the contract (‘aqd) or not: theory of fasād, theory of non-permeation of fasād, theory of detailed specification (tafṣīl). the proponents of the latter theory claim the total exclusion of the condition that causes disturbance in the basic components of the contr...

The classical condition number is a very rough measure of the effect of perturbations on the inverse of a square matrix. First, it assumes that the perturbation is infinitesimally small. Second, it does not take into account the perturbation structure (e.g., Vandermonde). Similarly, the classical notion of the inverse of a matrix neglects the possibility of large, structured perturbations. We d...

A necessary and sufficient condition is given for the exact reduction of systems modeled by linear fractional transformations (LFT’s) on structured operator sets. This condition is based on the existence of a rank-deficient solution to either of a pair of linear matrix inequalities which generalize Lyapunov equations; the notion of Gramians is thus also generalized to uncertain systems, as well...

This paper derives a stability condition for neural network control systems which the parameters of the controlled systems are uncertain. The stability condition can be imposed in training processes to guarantee the stability of the control systems. The controller is a single hidden layer, feedforward neural network. The controlled system is assumed to be full-state accessible and can be modele...

This paper is concerned with optimal control problem whose state equation is an uncertain differential equation. A necessary condition of optimality for uncertain optimal control problem is presented by using classical variational method. Meanwhile, an existence theorem of solution to backward uncertain differential equation is proved.

the paper discusses the location-allocation model for logistic networks and distribution centers through considering uncertain parameters. in real-world cases, demands and transshipment costs change over the period of the time. this may lead to large cost deviation in total cost. scenario based robust optimization approaches are proposed where occurrence probability of each scenario is not know...

In this paper, we mainly introduced a definition of moment exponential stability for multifactor uncertain differential equation. For illustrating of stability concept, several examples and counterexamples are given. Furthermore, a necessary and sufficient condition of stability in pth moment exponential of linear multifactor uncertain differential equation is obtained. Also, the necessary and ...