Hill method for linear periodic systems with delay

Abstract

The paper describes the application of the Hill method for stability investigations in frequency domain of retarded linear time-periodic (RLCP) systems. An alternative approach on basis of the periodized characteristic equation (PCE) is presented. In contrast to previous approaches to this problem, the PCE method avoids convergence problems and the need for solving transcendent equations. The key idea consists in relating the set of solutions with a Fredholm integral equation of the second kind. Then, applying the Fredholm theory allows to overcome the convergence problems. Moreover, a new set of formulae has been derived having improved computational properties. A comparison of the PCE and the Hill method shows the benefit of the new approach.