L2 gain analysis of linear parameter varying systems: dual problem and its finite dimensional approximation

In this paper, the L² gain analysis problem of linear parameter varying systems is studied. The primal/dual framework is exploited, and the duality theorem for an abstract linear programming problem with constraints described by an unbounded operator is established. If the system matrices are smooth in the scheduling parameter, the dual variables can be chosen from a separable space. This allows finite dimensional approximation without duality gap. Furthermore, when the system matrices are piecewise affine in the scheduling parameter, the problem can be cast as finite-dimensional LMI optimization problems.