Abstract

MARCANO, Cosme. Proposal of resolution of the matricial system in the second method of stability of Lyapunov. uct [online]. 2005, vol.9, n.35, pp.167-171. ISSN 1316-4821.

The Second Method of Stability of Lyapunov consists of selecting a so-called Lyapunov’s Candidate Function, which satisfies certain conditions that allows its use in the stability analysis of a mathematical model synthesized from a process which it want to put under the action of a given Control Law. In the case of linear systems, it is always possible to find a quadratic function, x^TAx, that satisfies the desired conditions. When applying the Second Stability Method of Lyapunov to this candidate function, it appears a matricial system of ordinary linear equations of the type A^TP + PA = -Q, where P and Q are nxn definite positive matrixes. In this work, the numeric solution of this algebraic system is proposed by solving a linear system of n2 unknown data and the same number of equations, which can be achieved, after some manipulation to the equations, with some traditional method, such as the Inverse Elimination of Gauss or any of its variants. This work shows two easy algorithms that allows re-accommodating the original matrix equation into the conventional form of a system of algebraic linear and ordinary equations.

Keywords : Gaussian Elimination; Matrix System; Second Stability Method of Lyapunov.