Extremal values of differential equations with application to control systems

Abstract

In the paper, maximal values xe(τ) of the solutions x(t) of the linear differential equations excited by the Dirac delta function are determined. The analytical solutions of the equations and also the maximal positive values of these solutions are obtained. The analytical formulae enable the design of the system with prescribed properties. The complementary case to the earlier paper is presented. In an earlier paper it was assumed that the roots si are different, and now we consider the case when s1 = s2 = … = sn.

Keywords

• extremal values
• characteristic equation
• transfer function
• dirac’s impulse
• multiple root