l1 Optimisation and shaping in finite settling time stabilising control

In this paper we consider some further performance requirements apart from tracking and disturbance rejection imposed on the family of Finite Settling Time Stabilising (FSTS) controllers of a plant P. In particular, using the complete parametrisation of the family of FSTS controllers it is shown how optimal controllers in the sense of minimising the l₁ or l_∞ norm of a certain error vector or shaping the error signal, control signal or input-output transfer function, can be constructed. This contribution examines the case of step inputs; the approach is algebraic and it reduces to the solution of a finite linear programme.