On Lyapunov functions and data-driven dissipativity

Abstract

Our contribution in this paper is twofold. In the first part, we study Lyapunov functions when a plant is interconnected with a dissipative stabilizing controller. In the second, we present results on data-driven approach to dissipative systems. In particular, we provide conditions under which an observed trajectory can be used to determine whether a system is dissipative with respect to a given supply rate. Our results are based on linear difference systems for which the use of quadratic difference forms play a central role for dissipativity and Lyapunov theory.

Data-driven dissipativity analysis: application of the matrix S-lemma

“…In [16] an iterative procedure was illustrated to compute the input feedforward passivity index and the shortage of passivity for discrete-time linear systems. The most relevant references for the problem studied in this paper are [17], [18], [19]. In [17], the notion of (finitehorizon) L-dissipativity was introduced and also studied in [18].…”

A geometric framework for constraints and data: from linear systems to convex processes

“…A particularly active area is the study of dissipativity on the basis of measured system trajectories, as seen in e.g. [22,113,143,144]. Extensions with regard to controllability are provided in [186].…”

“…The papers [106,125,178,188] deal with data-based controllability and observability analysis. Moreover, the problem of verifying dissipativity on the basis of measured system trajectories has been studied in [22,113,143,144].…”

“…More recently, there has also been an increasing interest in the problem of verifying dissipativity on the basis of system data. This problem has, for example, been addressed in [22,99,113,143].…”

From data and structure to models and controllers

“…The papers [111,155,232,248] deal with data-based controllability and observability analysis. Moreover, the problem of verifying dissipativity on the basis of measured system trajectories has been studied in several recent contributions, see [16,100,101,131,178,179].…”