We study the disturbance decoupling problem for linear time invariant descriptor systems. We give necessary and suucient conditions for the existence of a solution to the disturbance decoupling problem with/without stability via a proportional and/or derivative feedback that also makes the resulting closed-loop system regular and/or of index at most one. All results are proved constructively ba...

Necessary and sufficient conditions for exponential stability of linear time invariant delay differential-algebraic equations (DDAEs) are presented. The robustness of this property is studied when the equation is subjected to structured perturbations and a computable formula for the structured stability radius is derived. The results are illustrated by several examples.

Model reduction of large-scale linear time-invariant systems is an ubiquitous task in control and simulation of complex dynamical processes. We discuss how LQG balanced truncation can be applied to reduce the order of large-scale control problems arising from the spatial discretization of time-dependent partial differential equations. Numerical examples on a parallel computer demonstrate the ef...

In this paper, a class of linear systems with multiple time delays is studied. The problem of exponential stability of time-delay systems has been investigated by using Lyapunov functional method. We will convert the system of multiple time delays into a single time delay system and show that if the old system is stable then the new one is so. Then we investigate the stability of converted new ...

In this paper, we study the stabilization of nonlinear systems in critical cases by using the center manifold reduction technique. Three degenerate cases are considered, wherein the linearized model of the system has two zero eigenvalues, one zero eigenvalue and a pair of nonzero pure imaginary eigenvalues, or two distinct pairs of nonzero pure imaginary eigenvalues; while the remaining eigenva...

In this paper, we describe a parallel implementation of the implicitly coupled solution approach for combined electromechanical and electromagnetic transients simulation. In the proposed parallel-in-space-and-time scheme, the equations for transient stability (TS) are partitioned in space and the coupled-in-time electromagnetic transients equations (EMT) are partitioned in time. Thus each proce...

In this paper, we give a numerically reliable algorithm to compute the zeros of a periodic descriptor system. The algorithm is a variant of the staircase algorithm applied to the system pencil of an equivalent lifted time-invariant state-space system and extracts a low-order pencil which contains the zeros (both 6nite and in6nite) as well as the Kronecker structure of the periodic descriptor sy...

A commonly used distribution on the probability simplex is the Dirichlet distribution. In this paper we present the linear exponential family as an alternative. The distribution is known in the statistics community, but we present in this paper a numerically stable method to compute its parameters. Although the Dirichlet distribution is known to be a good Bayesian prior for probabilities we bel...

In this paper we show that for linear switching systems of the form xn+1 = Anxn + un+1, where the matrices An are chosen arbitrarily from a given set of matrices, bounded-input-bounded-output stability implies uniform exponential stability.