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Approximation of a linear dynamic process model using the frequency approach and a non-quadratic measure of the model error

Krzysztof B. Janiszowski (2014)

International Journal of Applied Mathematics and Computer Science

The paper presents a novel approach to approximation of a linear transfer function model, based on dynamic properties represented by a frequency response, e.g., determined as a result of discrete-time identification. The approximation is derived for minimization of a non-quadratic performance index. This index can be determined as an exponent or absolute norm of an error. Two algorithms for determination of the approximation coefficients are considered, a batch processing one and a recursive scheme,...

Approximation of control laws with distributed delays: a necessary condition for stability

Sabine Mondié, Michel Dambrine, Omar Santos (2002)

Kybernetika

The implementation of control laws with distributed delays that assign the spectrum of unstable linear multivariable systems with delay in the input requires an approximation of the integral. A necessary condition for stability of the closed-loop system is shown to be the stability of the controller itself. An illustrative multivariable example is given.

Approximation of fractional positive stable continuous-time linear systems by fractional positive stable discrete-time systems

Tadeusz Kaczorek (2013)

International Journal of Applied Mathematics and Computer Science

Fractional positive asymptotically stable continuous-time linear systems are approximated by fractional positive asymptotically stable discrete-time systems using a linear Padé-type approximation. It is shown that the approximation preserves the positivity and asymptotic stability of the systems. An optional system approximation is also discussed.

Approximation of Jacobian inverse kinematics algorithms

Krzysztof Tchoń, Joanna Karpińska, Mariusz Janiak (2009)

International Journal of Applied Mathematics and Computer Science

This paper addresses the synthesis problem of Jacobian inverse kinematics algorithms for stationary manipulators and mobile robots. Special attention is paid to the design of extended Jacobian algorithms that approximate the Jacobian pseudoinverse algorithm. Two approaches to the approximation problem are developed: one relies on variational calculus, the other is differential geometric. Example designs of the extended Jacobian inverse kinematics algorithm for 3DOF manipulators as well as for the...

Approximation of large-scale dynamical systems: an overview

Athanasios Antoulas, Dan Sorensen (2001)

International Journal of Applied Mathematics and Computer Science

In this paper we review the state of affairs in the area of approximation of large-scale systems. We distinguish three basic categories, namely the SVD-based, the Krylov-based and the SVD-Krylov-based approximation methods. The first two were developed independently of each other and have distinct sets of attributes and drawbacks. The third approach seeks to combine the best attributes of the first two.

Approximation of the Zakai equation in a nonlinear filtering problem with delay

Krystyna Twardowska, Tomasz Marnik, Monika Pasławska-Południak (2003)

International Journal of Applied Mathematics and Computer Science

A nonlinear filtering problem with delays in the state and observation equations is considered. The unnormalized conditional probability density of the filtered diffusion process satisfies the so-called Zakai equation and solves the nonlinear filtering problem. We examine the solution of the Zakai equation using an approximation result. Our theoretical deliberations are illustrated by a numerical example.

Argument increment stability criterion for linear delta models

Milan Hofreiter, Pavel Zítek (2003)

International Journal of Applied Mathematics and Computer Science

Currently used stability criteria for linear sampled-data systems refer to the standard linear difference equation form of the system model. This paper presents a stability criterion based on the argument increment rule modified for the delta operator form of the sampled-data model. For the asymptotic stability of this system form it is necessary and sufficient that the roots of the appropriate characteristic equation lie inside a circle in the left half of the complex plane, the radius of which...

Asymmetric recursive methods for time series

Tomáš Cipra (1994)

Applications of Mathematics

The problem of asymmetry appears in various aspects of time series modelling. Typical examples are asymmetric time series, asymmetric error distributions and asymmetric loss functions in estimating and predicting. The paper deals with asymmetric modifications of some recursive time series methods including Kalman filtering, exponential smoothing and recursive treatment of Box-Jenkins models.

Asymptotic analysis and control of a hybrid system composed by two vibrating strings connected by a point mass

C. Castro (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We consider a hybrid, one-dimensional, linear system consisting in two flexible strings connected by a point mass. It is known that this system presents two interesting features. First, it is well posed in an asymmetric space in which solutions have one more degree of regularity to one side of the point mass. Second, that the spectral gap vanishes asymptotically. We prove that the first property is a consequence of the second one. We also consider a system in which the point mass is replaced...

Asymptotic null controllability of bilinear systems

Fritz Colonius, Wolfgang Kliemann (1995)

Banach Center Publications

The region of asymptotic null controllability of bilinear systems with control constraints is characterized using Lyapunov exponents. It is given by the cone over the region of attraction of the maximal control set in projective space containing zero in its spectral interval.

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