Data-Driven Dissipativity Conditions for General Quadratic Supply Rate Function

The notion of dissipativity is immensely important for system analysis and controller design. In this paper, we formulate data-driven conditions for verifying dissipativity properties of a discrete linear time invariant dynamical system. Most data-driven conditions in the literature guarantee dissipativity only for a finite interval of time. Also, most data-driven methods that guarantee dissipativity consider what is referred to as the ($Q, S, R$) supply rate. We derive our data-driven dissipativity conditions for general supply rates which involve time differences of measured data. Moreover, our data-driven conditions guarantee dissipativity for infinite time horizon. We make use of the behavioral framework of dynamical systems and the notion of quadratic difference forms (QdFs) to formulate our data-driven dissipativity conditions as they help in generalizing the notion of dissipativity to general supply rates. Moreover, formulation of our data-driven dissipativity conditions does not require assuming persistence of excitation of measured data, which is a necessary assumption in formulation of data-driven dissipativity conditions proposed in the literature.