Finite settling time stabilisation: the robust SISO case

This paper deals with the problem of robustness to multiplicative plant perturbations for the case of Finite Settling Time Stabilization (FSTS) of SISO, linear, discrete–time systems. FSTS is a generalization of the deadbeat control and as in the case of deadbeat control the main feature of FSTS is the placement of all closed–loop poles at the origin of the z–plane. This makes FSTS sensitive to plant perturbations hence, the need of robust design. An efficient robustness index is introduced and the problem is reduced to a finite linear program where all the benefits of the simplex method, such as effectiveness, efficiency and ability to provide complete solution to the optimization problem, can be exploited.