On dissipativity, passivity and dynamic operability of nonlinear processes

Passivity and dissipativity have long being important tools in nonlinear systems analysis and control design. In this article, connections between dissipativity and the dynamic operability of nonlinear processes are explored. In particular, we study nonlinear processes that are dissipative with respect to a supply rate quadratic in the inputs and outputs. These type of dissipative systems include processes that can be unstable and can have unstable zero dynamics. Two methods to quantify operability are proposed. The first method analyses the speed of response of the closed-loop with no exogenous signals. The second method studies the output disturbance attenuation problem. The proposed framework reveals important insights into those nonlinear process characteristics that can limit dynamic operability.