LMI approach for ℋ∞ linear parameter-varying state feedback control

Abstract

Linear matrix inequality conditions are given for the existence of a stabilising linear parameter dependent state feedback gain for continuous time-varying systems in convex polytopic domains. Although there exist several results dealing with this problem in the literature, up to now all approaches assume that some matrices describing the system must be constant and/or must satisfy structural constraints. Here, all the system matrices are assumed to be affected by time-varying uncertainties and there are no structural constraints. The strategy proposed is much simpler than standard gain scheduling techniques, being specially adequate for systems with parameters that have unbounded or a priori unknown rates of variation, for instance, switched systems. Moreover, the conditions can also assure a guaranteed ℋ∞ attenuation level for the closed-loop system under arbitrarily fast parameter variations significantly improving the results based on a fixed gain obtained through quadratic stabilisability conditions. Numerical examples illustrate the use of the proposed control design with applications to two physical systems: a linear model of a helicopter subject to actuator failures and an electrical circuit used as a lowpass filter in the output stage of power converters.