Applications of the methods of weighted residuals in system science

Abstract

Piecewise linear functions arc applied to solve the state equations of linear system science with the introduction of the methods of weighted residuals (MWR). There are four different weighted procedures of MWR to be derived: (a) collocation, (b) subdomain, (c) Galerkin's and (d) least-squares methods. Applying the MWR, a linear system can be represented by a set of simultaneous linear algebraic equations, and a recursive algorithm and/or an operational matrix are available. Analysis and parameter identification of stale space equations of linear systems can thus be converted into a set of linear algebraic equations and solved using a recursive algorithm.