Stability criteria for rate limited Lur'e systems with connections to magnitude limits and anti-windup

This paper considers the stability of asymptotically stable linear systems subject to actuator rate constraints. The rate limit constraint is modelled by a first order feedback system with magnitude saturation and an integrator. Exploiting the ability to analytically derive the partial fraction expansion of the integrator modes, stability criteria are derived in terms of LMIs by expressing the system in Popov's indirect control form. The stability criteria are compared to those for magnitude limited systems, and it is shown that under certain conditions the LMI conditions for global asymptotic stability (GAS) with magnitude limits ensure GAS with rate limits. An interpretation of the results in terms of anti-windup (AW) control is presented, with IMC AW control shown to provide GAS for magnitude and rate saturation. The results provide constructive theory for the stabilisation of rate limited systems, and insight into the effect of using convex but conservative design theory, as is currently standard, on the properties of Lur'e systems.