On a linear differential equation of the advanced type

A linear differential equation of the advanced type is considered. Existence of solutions for any finite interval is shown. Also, a method for generating all the solutions is described and justified

Nonparametric Modeling and Model-Based Control of the Insulin-Glucose System

Non

A cone programming approach to the bilinear matrix inequality problem and its geometry

We discuss an approach for solving the Bilinear Matrix Inequality (BMI) based on its connections with certain problems defined over matrix cones. These problems are, among others, the cone generalization of the linear programming (LP) and the linear complementarity problem (LCP) (referred to as the Cone-LP and the Cone-LCP, respectively). Specifically, we show that solving a given BMI is equivalent to examining the solution set of a suitably constructed Cone-LP or Cone-LCP. This approach facilitates our understanding of the geometry of the BMI and opens up new avenues for the development of the computational procedures for its solution.

Kalman Filtering for a Generalized Class of Nonlinear Systems and a New Gaussian Quadrature Technique

The class of nonlinear systems treated in this technical note consists of the discrete time nonlinear systems that are formed by the interconnection of linear systems through static nonlinearities with few inputs. This special structure is exploited to reduce the dimension of the integrals involved in the propagation of mean values and covariances, thus permitting accurate calculations. Furthermore, a new quadrature scheme suitable for nonlinear Kalman filtering is introduced. The proposed techniques are applied to a seven-dimensional numerical example. The results show that they can increase the performance significantly