Determining Passivity via Quantifier Elimination

Assuring passivity of a closed loop control system is an important issue for the synthesis of the systems. In the present study, a new approach is proposed in order to determine the controller and system parameter spaces that guarantee the passivity of a given nonlinear input affine MIMO system. The utilized parameter space mapping is solving the classical passivity conditions by quantifier elimination. Therefore, the proposed method ensures the passivity of a system with respect to whole classes of function candidates as storage functions, instead of testing the passivity with respect to a single particular storage function. By using the proposed method, the overall computational complexity can be reduced significantly (in comparison to Lyapunov based approaches) by subdividing systems into subsystems and examine their passivity individually. Three benchmark case studies are discussed at the end of the present study in order to verify the effectiveness and correctness of the proposed method.