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O stabilności dyskretnych i ciągłych układów liniowych o zmiennych skokowo współczynnikach*

Bal A.

Zeszyty Naukowe. Automatyka / Politechnika Śląska

2008

z. 151

11-18

W pracy przedstawiono problem stabilności dla dyskretnych i ciągłych układów liniowych o zmiennych współczynnikach w czasie, w których funkcja przełączająca jest przedziałami stała. Dla takich układów wyznaczone zostały warunki stabilności za pomocą wykładników Lapunowa.

In this paper stability of discrete and continuous time-varying linear systems with piecewise constant switching signal is presented. For such systems the stability conditions are proposed with the aid of Lapunov exponent.

Stabilization of Second-order Systems by Non-linear Feedback

Skruch P.

International Journal of Applied Mathematics and Computer Science

2004

Vol. 14, no 4

455-460

A stabilization problem of second-order systems by non-linear feedback is considered. We discuss the case when only position feedback is available. The non-linear stabilizer is constructed by placing actuators and sensors in the same location and by using a parallel compensator. The stability of the closed-loop system is proved by LaSalle's theorem. The distinctive feature of the solution is that no transformation to a first-order system is invoked. The results of analytic and numerical computations are included to verify the theoretical analysis and the mathematical formulation.

Stable and related matrices in economic theory

Giorgi G.

Control and Cybernetics

2003

Vol. 32, no 2

397-410

It is well known that local stability analysis of a Walrasian multiple markets model is performed by approximating, according to Taylor's expansion, a system of first-order differential equations. So, one has to study the stability of a linear system (with constant coefficients). Since the earlier studies of Walrasian economic equilibrium, economists have suggested numerous conditions ensuring local stability of the same. The aim of this note is to give a survey of various conditions, used in economic analysis, ensuring that a (real) square matrix is stable. We show, in a unified manner, their inter-relations and make some new remarks on quasi-dominant matrices and on D-stable matrices.