Search results for "Exponent"
showing 10 items of 896 documents
Robust reliable control of uncertain discrete impulsive switched systems with state delays
2013
Published version of an article in the journal: Mathematical Problems in Engineering. Also available from the publisher at: http://dx.doi.org/10.1155/2013/197819 Open access This paper is concerned with the problem of robust reliable control for a class of uncertain discrete impulsive switched systems with state delays, where the actuators are subjected to failures. The parameter uncertainties are assumed to be norm-bounded, and the average dwell time approach is utilized for the stability analysis and controller design. Firstly, an exponential stability criterion is established in terms of linear matrix inequalities (LMIs). Then, a state feedback controller is constructed for the underlyin…
Confidence Intervals for the Mean Based on Exponential Type Inequalities and Empirical Likelihood
2013
For independent observations, recently, it has been proposed to construct the confidence intervals for the mean using exponential type inequalities. Although this method requires much weaker assumptions than those required by the classical methods, the resulting intervals are usually too large. Still in special cases, one can find some advantage of using bounded and unbounded Bernstein inequalities. In this paper, we discuss the applicability of this approach for dependent data. Moreover, we propose to use the empirical likelihood method both in the case of independent and dependent observations for inference regarding the mean. The advantage of empirical likelihood is its Bartlett correcta…
Passivity-based output feedback control of Markovian jump systems with discrete and distributed time-varying delays
2013
In this article, we present a new method in designing mode-dependent passivity-based output feedback controllers for Markovian jump systems with time-varying delays. Both discrete and distributed delays are considered in the model. A Lyapunov–Krasovskii function is constructed to establish new required sufficient conditions for ensuring exponentially mean-square stability and the passivity criteria, simultaneously. The method produces linear matrix inequality formulation that allows obtaining controller gains based on a convex optimisation method. Finally, a numerical example is given to illustrate the effectiveness of our approach.
A passivity approach to control of Markovian jump systems with mixed time-varying delays
2013
This paper investigated the problem of control design for a class of stochastic systems with Markovian jump parameters and time-varying delays. For the model under consideration, a passivity-based approach is introduced for designing mode-dependent output feedback controllers with mixed discrete and distributed delays. A Lypunov-Krasovskii function (LKF) is defined to establish new required sufficient conditions for ensuring exponentially mean-square stability and the passivity criteria, simultaneously. Moreover, controller gains are calculated based on a convex optimization method by solving a Linear Matrix Inequality (LMI). Finally, simulation results are provided to illustrate the effect…
Delay-Range-Dependent Linear Matrix Inequality Approach to Quantized H∞ Control of Linear Systems with Network-Induced Delays and Norm-Bounded Uncert…
2010
This paper deals with a convex optimization approach to the problem of robust network-based H∞ control for linear systems connected over a common digital communication network with static quantizers. Both the polytopic and the norm-bounded uncertainties are taken into consideration separately. First, the effect of both the output quantization levels and the network conditions under static quantizers is investigated. Second, by introducing a descriptor technique, using a Lyapunov—Krasovskii functional and a suitable change of variables, new required sufficient conditions are established in terms of delay-range-dependent linear matrix inequalities for the existence of the desired network-bas…
A spreadsheet modeling approach to the Holt–Winters optimal forecasting
2001
Abstract The objective of this paper is to determine the optimal forecasting for the Holt–Winters exponential smoothing model using spreadsheet modeling. This forecasting procedure is especially useful for short-term forecasts for series of sales data or levels of demand for goods. The non-linear programming problem associated with this forecasting model is formulated and a spreadsheet model is used to solve the problem of optimization efficiently. Also, a spreadsheet makes it possible to work in parallel with various objective functions (measures of forecast errors) and different procedures for calculating the initial values of the components of the model. Using a scenario analysis, the se…
Self-stabilizing Balls & Bins in Batches
2016
A fundamental problem in distributed computing is the distribution of requests to a set of uniform servers without a centralized controller. Classically, such problems are modelled as static balls into bins processes, where m balls (tasks) are to be distributed to n bins (servers). In a seminal work, [Azar et al.; JoC'99] proposed the sequential strategy Greedy[d] for n = m. When thrown, a ball queries the load of d random bins and is allocated to a least loaded of these. [Azar et al.; JoC'99] showed that d=2 yields an exponential improvement compared to d=1. [Berenbrink et al.; JoC'06] extended this to m ⇒ n, showing that the maximal load difference is independent of m for d=2 (in contrast…
Signal Restoration via a Splitting Approach
2012
International audience; In the present study, a novel signal restoration method from noisy data samples is presented and is termed as "signal split (SSplit)" approach. The new method utilizes Stein unbiased risk estimate estimator to split the signal, the Lipschitz exponents to identify noise elements and a heuristic approach for the signal reconstruction. However, unlike many noise removal techniques, the present method works only in the non-orthogonal domain. Signal restoration was performed on each individual part by finding the best compromise between the data samples and the smoothing criteria. Statistical results are quite promising and suggest better performance than the conventional…
A Cornucopia of Carnot groups in Low Dimensions
2022
Abstract Stratified groups are those simply connected Lie groups whose Lie algebras admit a derivation for which the eigenspace with eigenvalue 1 is Lie generating. When a stratified group is equipped with a left-invariant path distance that is homogeneous with respect to the automorphisms induced by the derivation, this metric space is known as Carnot group. Carnot groups appear in several mathematical contexts. To understand their algebraic structure, it is useful to study some examples explicitly. In this work, we provide a list of low-dimensional stratified groups, express their Lie product, and present a basis of left-invariant vector fields, together with their respective left-invaria…
The Riemannian manifold of all Riemannian metrics
1991
In this paper we study the geometry of (M, G) by using the ideas developed in [Michor, 1980]. With that differentiable structure on M it is possible to use variational principles and so we start in section 2 by computing geodesics as the curves in M minimizing the energy functional. From the geodesic equation, the covariant derivative of the Levi-Civita connection can be obtained, and that provides a direct method for computing the curvature of the manifold. Christoffel symbol and curvature turn out to be pointwise in M and so, although the mappings involved in the definition of the Ricci tensor and the scalar curvature have no trace, in our case we can define the concepts of ”Ricci like cu…