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Linear Differential Equation (linear + differential_equation)
Selected AbstractsRobust ,, filtering for uncertain differential linear repetitive processesINTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 3 2008Ligang Wu Abstract The unique characteristic of a repetitive process is a series of sweeps or passes through a set of dynamics defined over a finite duration known as the pass length. At the end of each pass, the process is reset and the next time through the output, or pass profile, produced on the previous pass acts as a forcing function on, and hence contributes to, the dynamics of the new pass profile. They are hence a class of systems where a variable must be expressed in terms of two directions of information propagation (from pass-to-pass and along a pass, respectively) where the dynamics over the finite pass length are described by a matrix linear differential equation and from pass to pass by a discrete updating structure. This means that filtering/estimation theory/algorithms for, in particular, 2D discrete linear systems is not applicable. In this paper, we solve a general robust filtering problem with a view towards use in many applications where such an action will be required. Copyright © 2007 John Wiley & Sons, Ltd. [source] The Price-Volatility Feedback Rate: An Implementable Mathematical Indicator of Market StabilityMATHEMATICAL FINANCE, Issue 1 2003Emilio Barucci Geometric analysis of iterated cross-volatilities of asset prices is adopted to assess the stability of the (risk-free) measure under infinitesimal perturbations. Perturbations of asset prices evolve through time according to an ordinary linear differential equation (hedged transfer). The decay (feedback) rate is explicitly computed through a Fourier series method implemented on high frequency time series. [source] On the complex oscillation theory of f , + A (z)f = 0 where A (z) is analytic in the unit discMATHEMATISCHE NACHRICHTEN, Issue 6 2009Ting-Bin Cao Abstract In this paper, we investigate the complex oscillation theory of the second order linear differential equation f , + A (z)f = 0, where the coefficient A (z) is an analytic function in the unit disc , = {z: |z | < 1} (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] On a linear differential equation with a proportional delayMATHEMATISCHE NACHRICHTEN, Issue 5-6 2007ermák Abstract This paper deals with the delay differential equation We impose some growth conditions on c, under which we are able to give a precise description of the asymptotic properties of all solutions of this equation. Although we naturally have to distinguish the cases c eventually positive and c eventually negative, we show a certain resemblance between the asymptotic formulae corresponding to both cases. Moreover, using the transformation approach we generalize these results to the equation with a general form of a delay. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Reduced order state-space models from the pulse responses of a linearized CFD schemeINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 6 2003Ann L. Gaitonde This paper describes a method for obtaining a time continuous reduced order model (ROM) from a system of time continuous linear differential equations. These equations are first put into a time discrete form using a finite difference approximation. The unit sample responses of the discrete system are calculated for each system input and these provide the Markov parameters of the system. An eigenvalue realization algorithm (ERA) is used to construct a discrete ROM. This ROM is then used to obtain a continuous ROM of the original continuous system. The focus of this paper is on the application of this method to the calculation of unsteady flows using the linearized Euler equations on moving meshes for aerofoils undergoing heave or linearized pitch motions. Applying a standard cell-centre spatial discretization and taking account of mesh movement a continuous system of differential equations is obtained which are continuous in time. These are put into discrete time form using an implicit finite difference approximation. Results are presented demonstrating the efficiency of the system reduction method for this system. Copyright © 2003 John Wiley & Sons, Ltd. [source] Nonlinear Modeling and Tracking Control of a Hydraulic Rotary Vane ActuatorPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2005Frank Heidtmann Rotary vane actuators as rotational drives provide rotational movements directly because they are constructed as a joint and actuator in one. So it is possible to pass on the disadvantageous transmission kinematics used with the so far usual differential cylinders at the arms of large manipulators. However, the use of hydraulic rotary vane actuators is associated with high internal oil leakage and/or high friction. Therefore, a nonlinear dynamic model for such an actuator, driving a rigid robot arm, as well as its nonlinear control are derived. To achieve tracking control a model based control law is set up using fundamental linear differential equations for the tracking error. The control law is implemented and tested on a testbed, the produced experimental results are presented. The same control algorithm can also be used to realize nonlinear disturbance attenuation for hydraulic rotary vane actuators via tracking control. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] | ||||||||||