A new algorithm for designing piecewise-linear scheduled gains with a minimal number of grid points

This paper proposes an algorithm for designing gain scheduled state feedback controllers that guarantee L₂ gain performance with a minimal number of grid points. A derived gain is composed of piecewise-linear functions of a scheduling parameter, which is desirable for implementability considering the often limited processing resources of embedded control computers. The algorithm is iterative: at each step a scheduled gain is designed, the “importance” of each grid point is evaluated, and the least important grid point is eliminated. As a result, the derived gain is expected to have a minimal number of grid points. An illustrative example shows how the gain is designed by the proposed algorithm.