Properties of analog systems with varying parameters [averaging/low-pass filters]

This paper examines the properties of solutions to ordinary differential equations from the point of view of their applications as averaging and low-pass filters. The stationarity of solutions to systems with varying parameters was analyzed together with stability conditions of these systems by making use of the theorem on stability of nonhomogeneous systems when the corresponding homogeneous systems were stable. The transient state was analyzed and the possibility of its shortening was shown. The performed simulations of the variable parameter Butterworth, Legendre and Chebyshev low-pass filters of the 2-nd up to the 6-th order proved the usefulness of the method.