LPV control and analysis under uncertain initial conditions

This paper is focused on the control of discrete-time linear parameter-varying (LPV) systems with uncertain initial conditions. The synthesis objective is to design a feedback LPV controller that ensures that the closed-loop system is asymptotically stable and some performance inequality is satisfied for all permissible parameter trajectories. The performance measure used is similar to the ℓ2-induced norm except that the initial state and the disturbance input are considered to reside in two separate norm balls; that is, the supremum of the ℓ2-norm of the performance output is minimized subject to the initial state taking values in a unit Euclidean ball and the disturbance input taking values in a unit ℓ2-norm ball. The paper provides convex analysis and synthesis conditions for solving this problem and demonstrates that using nonstationary LPV controllers instead of standard LPV ones could result in a significantly improved performance. The paper also shows how to determine bounding envelopes for the performance output using the analysis result. An illustrative example concludes the paper.