Induced L2 Norm Improvement by Interpolating Controllers for Discrete-time LPV Systems

The paper shows an interpolation-based control solution as a possible technique to formulate the constrained H∞ control problem for discrete-time linear parameter varying (LPV) systems. The control policy is constructed by interpolating among a priori designed, unconstrained, constant, state feedback controllers. Invariant set theory is used to introduce the measure of the domain of applicability. It is shown that the ‘trade-off’ between the performance and the size of the domain of applicability can be significantly reduced by controller interpolation. Hence, the interpolation-based controller becomes applicable over a much larger region than any other single state feedback. The proposed method gives stabilizing solution not only under hard constraints, but also allows the online modification of the induced L2 norm from the generalized disturbance input to the predefined performance output. Moreover, the suggested method can be applied in real-time environment.