Dissipativity-Based Output-Feedback Control for a Class of Semilinear Unstable Heat Equations

Abstract

The problem of output-feedback control for a class of semilinear unstable heat equations is addressed within the framework of dissipativity theory. It is shown that using a simple proportional output-feedback control in a collocated input-output pairing the closed-loop stability is ensured if the control gain is chosen sufficiently large and the nonlinearity satisfies a quadratic dissipativity condition. The approach is illustrated using numerical simulations.