H2H∞ optimal control synthesis with an α-shifted pole constraint

It is shown that it is possible to construct an α-shifted augmented system which is twice that of the original system such that the exact H₂ norm is preserved. An algorithm is developed that calculates the decentralized repeated gains. Based on numerical results, it is concluded that the new approach yields lower costs than Anderson and Moore´s approach (B.D.O. Anderson, J.B. Moore, 1989), in the sense that both the state and control costs are smaller. In principle, the approach is applicable to more general constraint regions, e.g., circular region, parabolic region, etc