Exact transient and steady state analyses of linear systems with periodic inputs

The calculation of the transient and steady state responses of linear systems to nonsinusoidal periodic inputs is of fundamental importance both from the practical and the theoretical points of view in electronic and power systems. The authors describe a new method for solving the problem. They review existing methods for computing the steady-state response and point out their limitations. A new method is presented which gives exact answers to the transient and the steady state responses in explicit forms. The method is extended to nth order linear systems, using the state variable approach. A complete numerical example of a second-order system with complex natural frequencies is included.<>