Backstepping-based stabilization of the pool-boiling system: An application of the circle criterion

We deal with the problem of the stabilization of the nonlinear PDE system that represents a pool boiling under a feedback loop. Toward this end, first we study well-posedness by discussing the choice of the appropriate space of functions, where the problem is cast. Second, we focus on various examples of backstepping feedback laws that can ensure stability and analyze them by using Popov-like theorems based on the circle criterion. Third, simulation results are reported to illustrate the findings of the theoretical investigation.

I. Introduction

For linear systems described by partial differential equations (PDEs) the choice of the feedback operator is often a difficult task, as it affects the location of an infinite spectrum on the complex plane. The problem is even more challenging for nonlinear distributed parameter systems (DPSs). Indeed, in this paper attention is devoted to an example of nonlinear DPS, the pool-boiling (PB) system with the goal of designing a feedback law for its stabilization.