In this report, the impulse response boundary of discrete-time, linear, time-invariant systems with interval uncertainty is studied. The key problem of determining the impulse response of such systems is to find the boundaries of the power of an interval matrix at a specified order. To estimate the bounds of the power of an interval matrix, interval perturbation theory is used. Two different me...

In this article we study a piecewise linear discretization schemes for transfer operators (Perron-Frobenius operators) associated with interval maps. We show how these can be used to provide rigorous pointwise approximations for invariant densities of Markov interval maps. We also derive the order of convergence of the approximate invariant density to the real one in the L∞-norm. The outcome of...

We consider uncertain fractional-order linear time invariant (FO-LTI) systems with interval coefficients. Our focus is on the robust controllability issue for interval FO-LTI systems in statespace form. We re-visited the controllability problem for the case when there is no interval uncertainty. It turns out that the stability check for FO-LTI systems amounts to checking the conventional intege...

We prove that, under a mild summability condition on the growth of the derivative on critical orbits any piecewise monotone interval map possibly containing discontinuities and singularities with infinite derivative (cusp map) admits an ergodic invariant probability measures which is absolutely continuous with respect to Lebesgue measure.

The problem of estimating the parameters of a nonlinear model from prior knowledge, experimental data and collateral requirements is viewed as one of set inversion, which is solved in an approximate but guaranteed way with the tools of interval analysis. It is, for instance, possible to characterize the set of all parameter vectors that are consistent with the data in the sense that the errors ...

It is shown that, for any time-invariant exponentially stable linear systemwith additive disturbances, time-varying exponentially stable interval observers can be constructed. The technique of construction relies on the Jordan canonical form that any real matrix admits and on time-varying changes of coordinates for elementary Jordan blocks which lead to cooperative linear systems. The approach ...

In sensitivity analysis one wants to know how the problem and the optimal solutions change under the variation of the input data. We consider the case when variation happens in the right hand side of the constraints and/or in the linear term of the objective function. We are interested to find the range of the parameter variation in Convex Quadratic Optimization (CQO) problems where the support...

interpretation is a good method for deriving loop invariants, but, unfortunately, it does not work well with disjunctions. This is where the technique of the paper is supposed to help. The idea is to use a theorem prover to show that the assertion never fails for the set of traces corresponding to the second disjunct (N mod 2 6= 0). Thus the abstract interpreter can be run on the abstract state...

We prove that an algebraic curve of genus g admits a representation by the interval exchange transformation. This representation is based on the “zippered rectangles” technique due to W. Veech. The invariants Oλ and θλ of the interval exchange transformation are shown to be the projective invariants of the curve C. We establish a Riemann–Roch formula for Oλ. The first steps to the classificatio...