Title :
Hill method for linear periodic systems with delay
Author :
Lampe, B.P. ; Rosenwasser, E.N. ; Berg, L.
Author_Institution :
Fac. of Comput. Sci. & Electr. Eng., Univ. of Rostock, Rostock, Germany
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.
Keywords :
convergence; delays; integral equations; linear systems; stability; time-varying systems; Fredholm integral equation; Fredholm theory; Hill method; convergence problems; delay; frequency domain; periodized characteristic equation; retarded linear time periodic systems; stability investigations; transcendent equations; Asymptotic stability; Convergence; Equations; Integral equations; Kernel; Stability criteria; Approximate analysis; Characteristic equation; Continuous systems; Delay elements; Integral equations; Periodic structures; Polynomials; Transfer functions;
Conference_Titel :
Methods and Models in Automation and Robotics (MMAR), 2011 16th International Conference on
Conference_Location :
Miedzyzdroje
Print_ISBN :
978-1-4577-0912-8
DOI :
10.1109/MMAR.2011.6031325
