Speaker
Description
We present a novel passivity enforcement (passivation) method for linear time-invariant systems based on the Kalman-Yakubovich-Popov (KYP) lemma and the closely related Lur'e equations. The passivation problem in our framework corresponds to finding a perturbation to a given non-passive system that renders the system passive while minimizing the $\mathcal{H}_2$-norm distance between the original non-passive and the resulting passive system. We show that this problem can be formulated as an unconstrained optimization problem whose objective function can be differentiated efficiently even in large-scale settings. To solve the resulting numerical optimization problem efficiently, we propose an initialization strategy based on modifying the feedthrough term and a restart strategy when it is likely that the optimization has converged to a non-global local minimum. Numerical examples illustrate the effectiveness of the proposed method.