Control of Polytopic LPV Systems with Uncertain Initial Conditions

This paper focuses on the control design and analysis for nonstationary linear parameter-varying systems with affine parameter dependence and uncertain initial conditions. The uncertain initial state and the disturbance input are allowed to reside in two separate norm balls. Convex analysis and synthesis conditions are derived, and a reachability analysis result for systems with pointwise-bounded inputs is developed, enabling the construction of ellipsoids in which the state or some output of interest lies at specified time instants. The usefulness of the proposed approach is demonstrated through an illustrative example involving a two-mass rotational system.