Ellipsoid

Random number generators for several distributions, both discrete and continuous, are here discussed and exemplified by scripts and examples. Random generation of uniform distributions is then applied to the problem of numerical integration in one or more dimensions. Convergent series are then derived for elliptic integrals and for the measure of the surface of the triaxial ellipsoid. Text in Italian.

In this paper we consider the finite-time stability problem for linear systems. Differently from previous papers, the stability analysis is performed with the aid of polyhedral Lyapunov functions rather than with the classical quadratic Lyapunov functions. In this way we are able to manage more realistic constraints on the state variables; indeed, in a way which is naturally compatible with polyhedral functions, we assume that the sets to which the state variables must belong in order to satisfy the finite-time stability requirement are boxes (or more in general polytopes) rather than ellipsoids. The main result, derived by using polyhedral Lyapunov functions, is a sufficient condition for finite-time stability of linear systems, which can also be used in the controller design context. Detailed analysis and design examples are presented to illustrate the advantages of the proposed methodology over existing methods.

... Among the theoretical tools available are stability theorems, such as the KAM theorem about perturbations of invariant tori and the energy-Casimir method (Holm et ... Ui ~ `1llUUJ~j ~41 JO OSfl1~OO~ Sq~UOJ S~X1~ Oq~ JO UO!PUUJ ~ind ~ si ad - A `°~ `Josu~i 1U~JOUi 0q3 JO ...

In the water resource management of a river basin, elevation values used in various calculations, hydraulic analysis, river building planning, flood control, irrigation planning and others must refer to the same elevation datum. The most suitable elevation datum in the water resource management of a river basin is geoid, and the most suitable elevation system is orthometric elevation system. The unification of elevation datum consists of the determination of its point origin, tide observation, and the installation of elevation datum network. The point origin is a permanent peg called peil installed next to the location of sea surface tide observation.Minimum tide observation is 29 days. Elevation datum network is a benchmark, installed systemically along the left and the right sides of the main river, tributary,around the irrigation development area, dam plan location, and others. The calculation of the height difference between benchmarks is conducted using precise levelling method.

The finite-time stability problem for state-dependent impulsive dynamical linear systems (SD-IDLS) is addressed in this note. SD-IDLS are a special class of hybrid systems which exhibit jumps when the state trajectory reaches a resetting set. A sufficient condition for finite-time stability of SD-IDLS is provided. S-procedure arguments are exploited to obtain a formulation of this sufficient condition which is numerically tractable by means of Differential Linear Matrix Inequalities. Since such a formulation may be in general more ...

Skin detection is an important part of face localization since the most exposed part of human skin is the face. This paper proposes a novel algorithm for face localization via skin detection. The algorithm utilizes a kernel iterative procedure to check for the region of interest in an image where it is likely that the face exists. The algorithm utilizes a swarm of particles in a kernel that randomly check the fitness of the corresponding pixel BGR value which is determined from a skin BGR dataset. Consequently, the kernel which has the best fitness value is chosen as the region of the image where it is likely that the face exists. Following this, we employ an active contour model called Snakes algorithm which further converges on our region of interest and finally a contour of the face region is extracted from the original image.

The domain of attraction of a class of fractional order systems subject to saturating actuators is investigated in this paper. We show the domain of attraction is the convex hull of a set of ellipsoids. In this paper, the Lyapunov direct approach and fractional order inequality are applied to estimating the domain of attraction for fractional order systems subject to actuator saturation. We demonstrate that the convex hull of ellipsoids can be made invariant for saturating actuators if each ellipsoid with a bounded control of the saturating actuators is invariant. The estimation on the contractively invariant ellipsoid and construction of the continuous feedback law are derived in terms of linear matrix inequalities (LMIs). Two numerical examples illustrate the effectiveness of the developed method.

Citation: Kai Chen, Junguo Lu, Chuang Li. The ellipsoidal invariant set of fractional order systems subject to actuator saturation: the convex combination form. IEEE/CAA Journal of Automatica Sinica, 2016, 3(3): 311-319

For a fine ferromagnetic particle of a non-ellipsoidal external shape, an effective single-domain diameter is defined as a characteristic length at which the energy of a stable quasi-uniform state (usually a flower state) of the particle coincides with that of the lowest non-uniform (`multi-domain') state. The effective single-domain diameters for soft magnetic parallelepipeds and cylinders having aspect ratios 0.5⩽m⩽3 are

The authors consider the problem of a target control for a discrete-time linear system with bounded disturbance input. The target is an ellipsoid in an n-dimensional Euclidean space. The nonlinear closed-loop strategies are calculated by employing the notion of a safety tube. The introduction of an auxiliary function allows the construction of the safety tube and evaluation of the control strategies. The latter take the form of two procedures, for the positions inside and outside the safety tube, respectively.<<ETX>>

Ellipsoids are proposed that contain optimal solutions of the primal and/or dual linear pro-gramming problem and do not depend on the method used to solve the original formulation. It is shown that many well-known interior-point methods realize descents toward the centers of ellipsoids. The con-structed ellipsoids are used to formulate criteria for identifying the optimal basic and nonbasic variables.

The physical properties of fruits in the agriculture industry constitute the main information in the quality determination for activities as exportation. This work presents a visual inspection based method for the classification of mango (Mangifera Indica L.). The classification process is made according to the Norma Tecnica Colombiana (Colombian Technical Norm) NTC 5139 standard, by means of automatic estimation of physical properties of fruits, such as height, width, volume, weight, caliber, and maturity level using the Principal Component Analysis and a fruit’s ellipsoidal 3-D model. Finally, the level of maturity is inferred through a similarity measure of the color distribution between the fruit and experimentally fixed models in the HSL space. The results showed that the method is computationally efficient, non invasive, precise and of low cost.