Minimisation of Transient Perturbation Growth in Linearised Lorenz Equations

This paper describes the LMI synthesis of feedback controllers which minimise closed loop transient perturbation growth with limited control effort. Controllers are synthesized for the linearised Lorenz equations, and their performance is compared to that of LQR controllers. At low control effort the controllers behave similarly, but the LMI based controllers are able to produce an almost monotonically falling transient with increasing control effort, whereas LQR controllers have a distinct minimum transient. Evidence is found that controllers which produce the lowest transients do not necessarily have the most orthogonal system eigenvectors, and an explanation in terms of modal and non-modal growth components is presented. Both LMI and LQR controllers are able to stabilise the full Lorenz equations for limited initial conditions.