Structured storage functions for cascaded systems

Dissipativity analysis is an important tool for the analysis of the dynamic response of systems of Ordinary Differential Equations to structural and parametric perturbations. In order to certify dissipativity, semi-definite programming is commonly used for the computation of storage functions of polynomial systems, but is currently not a practical solution for large-scale systems. This paper formulates the computation of a class of structured storage functions that exploit the structure of systems that can be decomposed into cascades. Structured storage functions allow the decomposition of the semi-definite programs used to prove dissipativity, thereby reducing the computational cost of SOS programming and making its application to large-scale systems more practical. Thus structured storage functions deliver additional speed and flexibility to the dissipativity approach to parametric and structural sensitivity analysis.