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...

this paper is pertained with the problem of admissibility analysis of uncertain discrete-time nonlinear singular systems by adopting the state-space takagi-sugeno fuzzy model with time-delays and norm-bounded parameter uncertainties. lyapunov krasovskii functionals are constructed to obtain delay-dependent stability condition in terms of linear matrix inequalities, which is dependent on the low...

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.

We introduce a new notion of algorithmic stability, which we call training stability. We show that training stability is sufficient for good bounds on generalization error. These bounds hold even when the learner has infinite VC dimension. In the PAC setting, training stability gives necessary and sufficient conditions for exponential convergence, and thus serves as a distribution-dependent ana...

We consider switched systems on Banach and Hilbert spaces governed by strongly continuous one-parameter semigroups of linear evolution operators. We provide necessary and sufficient conditions for their global exponential stability, uniform with respect to the switching signal, in terms of the existence of a Lyapunov function common to all modes.