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Similarity transformation of matrices to one common canonical form and its applications to 2D linear systems

Tadeusz Kaczorek (2010)

International Journal of Applied Mathematics and Computer Science

The notion of a common canonical form for a sequence of square matrices is introduced. Necessary and sufficient conditions for the existence of a similarity transformation reducing the sequence of matrices to the common canonical form are established. It is shown that (i) using a suitable state vector linear transformation it is possible to decompose a linear 2D system into two linear 2D subsystems such that the dynamics of the second subsystem are independent of those of the first one, (ii) the...

Simple conditions for practical stability of positive fractional discrete-time linear systems

Mikołaj Busłowicz, Tadeusz Kaczorek (2009)

International Journal of Applied Mathematics and Computer Science

In the paper the problem of practical stability of linear positive discrete-time systems of fractional order is addressed. New simple necessary and sufficient conditions for practical stability and for practical stability independent of the length of practical implementation are established. It is shown that practical stability of the system is equivalent to asymptotic stability of the corresponding standard positive discrete-time systems of the same order. The discussion is illustrated with numerical...

Simple environment for developing methods of controlling chaos in spatially distributed systems

Łukasz Korus (2011)

International Journal of Applied Mathematics and Computer Science

The paper presents a simple mathematical model called a coupled map lattice (CML). For some range of its parameters, this model generates complex, spatiotemporal behavior which seems to be chaotic. The main purpose of the paper is to provide results of stability analysis and compare them with those obtained from numerical simulation. The indirect Lyapunov method and Lyapunov exponents are used to examine the dependence on initial conditions. The net direction phase is introduced to measure the symmetry...

Simplification of the generalized state equations

Tanel Mullari, Ülle Kotta (2006)

Kybernetika

The paper studies the problem of lowering the orders of input derivatives in nonlinear generalized state equations via generalized coordinate transformation. An alternative, computation-oriented proof is presented for the theorem, originally proved by Delaleau and Respondek, giving necessary and sufficient conditions for existence of such a transformation, in terms of commutativity of certain vector fields. Moreover, the dual conditions in terms of 1-forms have been derived, allowing to calculate...

Simultaneous controllability in sharp time for two elastic strings

Sergei Avdonin, Marius Tucsnak (2001)

ESAIM: Control, Optimisation and Calculus of Variations

We study the simultaneously reachable subspace for two strings controlled from a common endpoint. We give necessary and sufficient conditions for simultaneous spectral and approximate controllability. Moreover we prove the lack of simultaneous exact controllability and we study the space of simultaneously reachable states as a function of the position of the joint. For each type of controllability result we give the sharp controllability time.

Simultaneous controllability in sharp time for two elastic strings

Sergei Avdonin, Marius Tucsnak (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We study the simultaneously reachable subspace for two strings controlled from a common endpoint. We give necessary and sufficient conditions for simultaneous spectral and approximate controllability. Moreover we prove the lack of simultaneous exact controllability and we study the space of simultaneously reachable states as a function of the position of the joint. For each type of controllability result we give the sharp controllability time.

Simultaneous Localization And Mapping: A feature-based probabilistic approach

Piotr Skrzypczyński (2009)

International Journal of Applied Mathematics and Computer Science

This article provides an introduction to Simultaneous Localization And Mapping (SLAM), with the focus on probabilistic SLAM utilizing a feature-based description of the environment. A probabilistic formulation of the SLAM problem is introduced, and a solution based on the Extended Kalman Filter (EKF-SLAM) is shown. Important issues of convergence, consistency, observability, data association and scaling in EKF-SLAM are discussed from both theoretical and practical points of view. Major extensions...

Simultaneous output-feedback stabilization for continuous systems in Banach spaces

Fouad M. AL-Sunni, Frank L. Lewis (1998)

Kybernetika

A design technique for the stabilization of M linear systems by one constant output-feedback controller is developed. The design equations are functions of the state and the control weighting matrices. An example of the stabilization of an aircraft at different operating points is given.

Simultaneous stabilization in A ℝ ( )

Raymond Mortini, Brett D. Wick (2009)

Studia Mathematica

We study the problem of simultaneous stabilization for the algebra A ℝ ( ) . Invertible pairs ( f j , g j ) , j = 1,..., n, in a commutative unital algebra are called simultaneously stabilizable if there exists a pair (α,β) of elements such that α f j + β g j is invertible in this algebra for j = 1,..., n. For n = 2, the simultaneous stabilization problem admits a positive solution for any data if and only if the Bass stable rank of the algebra is one. Since A ℝ ( ) has stable rank two, we are faced here with a different situation....

Simultaneous state and parameter estimation based actuator fault detection and diagnosis for an unmanned helicopter

Chong Wu, Juntong Qi, Dalei Song, Xin Qi, Jianda Han (2015)

International Journal of Applied Mathematics and Computer Science

Simultaneous state and parameter estimation based actuator fault detection and diagnosis (FDD) for single-rotor unmanned helicopters (UHs) is investigated in this paper. A literature review of actuator FDD for UHs is given firstly. Based on actuator healthy coefficients (AHCs), which are introduced to represent actuator faults, a combined dynamic model is established with the augmented state containing both the flight state and AHCs. Then the actuator fault detection and diagnosis problem is transformed...

Single input controllability of a simplified fluid-structure interaction model

Yuning Liu, Takéo Takahashi, Marius Tucsnak (2013)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we study a controllability problem for a simplified one dimensional model for the motion of a rigid body in a viscous fluid. The control variable is the velocity of the fluid at one end. One of the novelties brought in with respect to the existing literature consists in the fact that we use a single scalar control. Moreover, we introduce a new methodology, which can be used for other nonlinear parabolic systems, independently of the techniques previously used for the linearized problem....

Currently displaying 61 – 80 of 419