Control Design Using Passivation for Stability and Performance

A method to passivate a given system by using an input-output transformation matrix is introduced. This matrix generalizes the commonly used methods of series, feedback, and feedforward to passivate a linear or nonlinear system. Through an appropriate design of this matrix, positive passivity indices can be guaranteed for the system. Furthermore, this transformation matrix allows the use of a nonpassive system as a controller to guarantee the passivity and finite-gain L
₂
stability of a negative feedback configuration. The passivation parameters can be selected to improve system performance. The results are illustrated by considering nonlinear systems and linear systems with input/output delay. To validate the theory, simulation results in CarSim and Simulink are presented.