Control by symmetrisation of complex-valued dynamical systems

Linear state-space systems expressed in complex coordinates may include the complex conjugate when they are not symmetric . Although the original real system remains linear, the conjugate operator does not allow the model to be analysed as a standard complex-valued linear system. This paper proposes a methodology for designing controllers for asymmetric complex-valued dynamical systems. The proposed technique adds an element to the control algorithm that symmetrises the open-loop dynamics. Symmetrisation allows the use of standard tools for linear complex-valued systems. Illustrative examples and an application to three-phase electrical circuits are provided.