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Falseness of the finiteness property of the spectral subradius

Adam Czornik, Piotr Jurgas (2007)

International Journal of Applied Mathematics and Computer Science

We prove that there exist infinitely may values of the real parameter α for which the exact value of the spectral subradius of the set of two matrices (one matrix with ones above and on the diagonal and zeros elsewhere, and one matrix with α below and on the diagonal and zeros elsewhere, both matrices having two rows and two columns) cannot be calculated in a finite number of steps. Our proof uses only elementary facts from the theory of formal languages and from linear algebra, but it is not constructive...

Fault-tolerant control strategy for actuator faults using LPV techniques: Application to a two degree of freedom helicopter

Saúl Montes de Oca, Vicenç Puig, Marcin Witczak, Łukasz Dziekan (2012)

International Journal of Applied Mathematics and Computer Science

In this paper, a Fault Tolerant Control (FTC) strategy for Linear Parameter Varying (LPV) systems that can be used in the case of actuator faults is proposed. The idea of this FTC method is to adapt the faulty plant instead of adapting the controller to the faulty plant. This approach can be seen as a kind of virtual actuator. An integrated FTC design procedure for the fault identification and fault-tolerant control schemes using LPV techniques is provided as well. Fault identification is based...

Finite time stability and relative controllability of second order linear differential systems with pure delay

Mengmeng Li, Michal Fečkan, JinRong Wang (2023)

Applications of Mathematics

We first consider the finite time stability of second order linear differential systems with pure delay via giving a number of properties of delayed matrix functions. We secondly give sufficient and necessary conditions to examine that a linear delay system is relatively controllable. Further, we apply the fixed-point theorem to derive a relatively controllable result for a semilinear system. Finally, some examples are presented to illustrate the validity of the main theorems.

Fractional kalman filter algorithm for the states parameters and order of fractional system estimation

Dominik Sierociuk, Andrzej Dzieliński (2006)

International Journal of Applied Mathematics and Computer Science

This paper presents a generalization of the Kalman filter for linear and nonlinear fractional order discrete state-space systems. Linear and nonlinear discrete fractional order state-space systems are also introduced. The simplified kalman filter for the linear case is called the fractional Kalman filter and its nonlinear extension is named the extended fractional Kalman filter. The background and motivations for using such techniques are given, and some algorithms are discussed. The paper also...

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