38,895 research outputs found
An Overview of Polynomially Computable Characteristics of Special Interval Matrices
It is well known that many problems in interval computation are intractable,
which restricts our attempts to solve large problems in reasonable time. This
does not mean, however, that all problems are computationally hard. Identifying
polynomially solvable classes thus belongs to important current trends. The
purpose of this paper is to review some of such classes. In particular, we
focus on several special interval matrices and investigate their convenient
properties. We consider tridiagonal matrices, {M,H,P,B}-matrices, inverse
M-matrices, inverse nonnegative matrices, nonnegative matrices, totally
positive matrices and some others. We focus in particular on computing the
range of the determinant, eigenvalues, singular values, and selected norms.
Whenever possible, we state also formulae for determining the inverse matrix
and the hull of the solution set of an interval system of linear equations. We
survey not only the known facts, but we present some new views as well
Interval Prediction for Continuous-Time Systems with Parametric Uncertainties
The problem of behaviour prediction for linear parameter-varying systems is
considered in the interval framework. It is assumed that the system is subject
to uncertain inputs and the vector of scheduling parameters is unmeasurable,
but all uncertainties take values in a given admissible set. Then an interval
predictor is designed and its stability is guaranteed applying Lyapunov
function with a novel structure. The conditions of stability are formulated in
the form of linear matrix inequalities. Efficiency of the theoretical results
is demonstrated in the application to safe motion planning for autonomous
vehicles.Comment: 6 pages, CDC 2019. Website:
https://eleurent.github.io/interval-prediction
Exactly solvable models through the generalized empty interval method, for multi-species interactions
Multi-species reaction-diffusion systems, with nearest-neighbor interaction
on a one-dimensional lattice are considered. Necessary and sufficient
constraints on the interaction rates are obtained, that guarantee the
closedness of the time evolution equation for 's, the
expectation value of the product of certain linear combination of the number
operators on consecutive sites at time . The constraints are solved for
the single-species left-right-symmetric systems. Also, examples of
multi-species system for which the evolution equations of 's are closed, are given.Comment: 18 pages, LaTeX2e, no figure
Switched networks and complementarity
A modeling framework is proposed for circuits that are subject both to externally induced switches (time events) and to state events. The framework applies to switched networks with linear and piecewise-linear elements, including diodes. We show that the linear complementarity formulation, which already has proved effective for piecewise-linear networks, can be extended in a natural way to also cover switching circuits. To achieve this, we use a generalization of the linear complementarity problem known as the cone-complementarity problem. We show that the proposed framework is sound in the sense that existence and uniqueness of solutions is guaranteed under a passivity assumption. We prove that only first-order impulses occur and characterize all situations that give rise to a state jump; moreover, we provide rules that determine the jump. Finally, we show that within our framework, energy cannot increase as a result of a jump, and we derive a stability result from this
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