High-order Differential Dissipativity Analysis of Nonlinear Processes

Abstract

Dissipativity theory is an effective tool for system analysis and control design for network systems. Differential dissipativity is an extension of dissipativity achieved by lifting storage functions and supply rates to the tangent bundle. This paper extends differential dissipativity to the high order derivatives of the displacement of external variables. It allows for a more detailed description of nonlinear systems dynamics in terms of dissipativity, which can result in less conservative stability and performance conditions. It can be regarded either as a nonlinear extension of quadratic differential form (QDF) dissipativity for linear systems, or an extension of differential dissipativity to more detailed supply rates. Important features of dissipativity such as the determination of supply rate and storage function, stability conditions for open systems and interconnections for networked dynamics are investigated.