Dissipativity analysis for control affine systems in closed-loop with parameterized Jurdjevic-Quinn feedback controllers

This paper considers dissipativity-based analysis for control affine systems in closed-loop with damping feedback controllers. The approach is based on the computation of a locally-defined potential using a geometric decomposition of the drift vector field. The obtained potential is used to construct a damping feedback controller of the Jurdjevic-Quinn type. Dissipativity analysis of the controlled system is carried using an approximate realization of a target dissipative system to construct a storage function. The particular dissipative realization considered in the present paper is shown to exist under mild assumption on the Hessian of the computed potential which is locally-defined in a neighborhood of a desired equilibrium. The approach is then used to characterize excess or shortage of passivity of the closed-loop system, as parameterized by controller gains, which is a problem of interest in the context of decentralized control of interconnected systems. The proposed design approach is illustrated using an example.