Multi-input nonlinear affine systems represented in a canonical (normal) form are considered. The controls are assumed to be constrained. The application of feedback linearization results in a closed-loop system that is decomposed into an aggregate of independent linear subsystems in a neighborhood of the origin and is nonlinear when controls reach saturation. For the closed-loop system obtaine...

We investigate conditions for the existence of the limiting conditional distribution of a bivariate random vector when one component becomes large. We revisit the existing literature on the topic, and present some new sufficient conditions. We concentrate on the case where the conditioning variable belongs to the maximum domain of attraction of the Gumbel law, and we study geometric conditions ...

We call this a Chover-type LIL (laws of the iterated logarithm). This type LIL has been established by Vasudeva and Divanji [13], Zinchenko [14] for delayed sums, by Chen and Huang [3] for geometric weighted sums, and by Chen [2] for weighted sums. Qi and Cheng [11] extended the Chover-type law of the iterated logarithm for the partial sums to the case where the underlying distribution is in th...

Zusammenfassung Der Beitrag beschreibt ein LyapunovFunktionen-basiertes Führungsfilter für lineare Strecken mit Stellgrößenbegrenzung. Ziel des Filters ist es, die Abhängigkeit zwischen der zu stabilisierenden Ruhelage und der Größe des mit Lyapunov-Funktionen nachweisbaren Einzugsbereichs zu überwinden. Hierdurch kann erreicht werden, dass für alle Ruhelagen im System der gleiche Einzugsbereic...

By assuming that the underlying distribution belongs to the domain of attraction of an extreme value distribution, one can extrapolate the data to a far tail region so that a rare event can be predicted. However, when the distribution is in the domain of attraction of a Gumbel distribution, the extrapolation is quite limited generally in comparison with a heavy tailed distribution. In view of t...

We study the tail behavior of the distribution of the sum of asymptotically independent risks whose marginal distributions belong to the maximal domain of attraction of the Gumbel distribution. We impose conditions on the distribution of the risks (X, Y ) such that P (X + Y > x) ∼ (const)P (X > x). With the further assumption of non-negativity of the risks, the result is extended to more than t...

Abstract. In this paper we consider an additive functional of an observable V (x) of a Markov jump process. We assume that the law of the expected jump time t(x) under the invariant probability measure π of the skeleton chain belongs to the domain of attraction of a subordinator. Then, the scaled limit of the functional is a Mittag-Leffler proces, provided that Ψ(x) := V (x)t(x) is square integ...

We study the asymptotic behavior of the diameter or maximum interpoint distance of a cloud of i.i.d. d-dimensional random vectors when the number of points in the cloud tends to infinity. This is a non standard extreme value problem since the diameter is a max U -statistic, hence the maximum of dependent random variables. Therefore, the limiting distributions may not be extreme value distributi...

Based on a recent duality theory for linear differential inclusions (LDIs), the condition for stability of an LDI in terms of one Lyapunov function can be easily derived from that in terms of its conjugate function. This paper uses a particular pair of conjugate functions, the convex hull of quadratics and the maximum of quadratics, for the purpose of estimating the domain of attraction for sys...

For a linear system under a given saturated linear feedback, we propose feedback laws that achieve semi-global stabilization on the null controllable region while preserving the performance of the original feedback law in a 4xed region. Here by semi-global stabilization on the null controllable region we mean the design of feedback laws that result in a domain of attraction that includes any a ...