Analysis of stability for networks including converters

Stability is a very important property of control loop systems. For Linear Time Invariant (LTI) systems the Nyquist criterion is well known. In systems with converters, signals with different frequencies are related, these systems are not LTI. To describe them, the theory for Linear Time Periodic (LTP) systems can be used: The transfer function of the LTI systems is extended to the transfer matrix of LTP systems; the Nyquist criterion can also be extended for these systems using the eigenloci of the transfer matrix. Regarding Exponentially Modulated Periodic (EMP) signals as stationary solutions for LTI or LTP systems, an alternative approach is presented: The Nyquist criterion can be derivated using the relation between the Nyquist plot and the conformal map of the transfer function for LTI systems. With this, a transfer function of the open loop is defined also for LTP systems. As will be shown the Nyquist criterion can be applied to this transfer function for LTP systems.