Mixed L1/H2/H∞ control design:: numerical optimization approaches

This paper presents some new approaches to mixed performance control problems of linear systems. The design techniques proposed in this paper are based on numerical search of the norm bounded stable transfer matrix Q in the H-infinity and H-2 suboptimal controller parameterizations so that the additional performance specifications are satisfied. The design problems are then converted to some finite dimensional non-linear unconstrained optimization problems by explicitly parameterizing the H-infinity or H-2 norm bounded stable transfer matrix Q for any fixed order. Finally, some two-stage optimization algorithms are applied to find the optimal parameters. Numerical examples have shown significant performance improvements of the proposed algorithms over those in the existing literature.