An LPV Control Approach to Asymptotic Rejection of Non-stationary Disturbances with Guaranteed Worst-Case Performance

A linear parameter-varying controller synthesis procedure is developed for the asymptotic rejection of non-stationary infinite-energy disturbances generated by a parameter-dependent exo-system, while also guaranteeing a specified level of performance measured in terms of the worst- case energy amplification from a finite-energy disturbance to a performance output. The asymptotic regulation objective is achievable if a parameter-dependent system of differential algebraic equations admits bounded solutions for all possible parameter variations, which can be investigated by robust stability analysis techniques. Based on uniform bounds on the solutions, a suitable Lyapunov matrix can be constructed beforehand to achieve the additional performance objective by online scheduling, through LMI optimization, of a controller that accompanies a replica of the exo-system scheduled suitably via the solution of the differential algebraic regulator equations.