Bendixson's Criterion for Autonomous Systems with an Invariant Linear Subspace

AN ALGORITHM FOR FINDING THE STABILITY OF LINEAR TIME-INVARIANT SYSTEMS

The purpose of this paper is to show that the ideas and techniques of the classical methods of finding stability, such as the criteria of Leonhard and Nyquist, can be used to derive simple algorithm to verify stability. This is enhanced by evaluating the argument of the characteristic equation of a linear system in the neighbourhood of the origin of the complex plane along the imaginary axis

a new type-ii fuzzy logic based controller for non-linear dynamical systems with application to 3-psp parallel robot

abstract type-ii fuzzy logic has shown its superiority over traditional fuzzy logic when dealing with uncertainty. type-ii fuzzy logic controllers are however newer and more promising approaches that have been recently applied to various fields due to their significant contribution especially when the noise (as an important instance of uncertainty) emerges. during the design of type- i fuz...

On linear operators with an invariant subspace of functions

Let us denote V, the finite dimensional vector spaces of functions of the form ψ(x) = pn(x)+ f(x)pm(x) where pn(x) and pm(x) are arbitrary polynomials of degree at most n andm in the variable x while f(x) represents a fixed function of x. Conditions onm,n and f(x) are found such that families of linear differential operators exist which preserve V. A special emphasis is accorded to the cases wh...

An Invariant Subspace Theorem

for every rational function ƒ with poles off K. In this note it is shown that any operator for which the spectrum is a spectral set has a nontrivial invariant subspace. In [6] von Neumann introduced the notion of spectral set and showed that if T has II T\\ = 1 then the closed unit disc, D"~, is a spectral set for T. For this reason any operator whose spectrum is a spectral set is called a von ...

Subspace Identification for Linear Systems