Dissipativity Analysis for Linear Systems in the Behavioural Framework

Abstract

This paper develops some dissipativity conditions for linear time-invariant (LTI) systems in the behavioural framework. The behaviour of a system is characterised by its persistently exciting trajectories. For the dissipativity conditions, both the supply rate and the storage function are represented using quadratic difference forms (QdFs) using past steps. We show that it is possible to define an LTI system of arbitrary length using trajectories with low order of excitation. The system can be defined in a similar way as an image representation and the dissipativity conditions can hence be derived using a similar logic. The conditions are presented in the form of linear matrix inequalities (LMIs).