MULTIVARIABLE FINITE SETTLING TIME STABILISATION: PARAMETRISATION AND PROPERTIES

摘要

The problem of Finite Settling Time Stabilisation (FSTS) for multivariable, discrete-time systems is discussed in this paper. The approach is algebraic and the problem reduces to the solution of a polynomial Diophantine equation; many of the solvability conditions are expressed as standard linear algebra tests. A Kucera-Youla-Bonjiorno type parametrisation of the family of the FSTS controllers is obtained and necessary and sufficient conditions for strong FSTS are derived. Finally, solvability conditions for FST tracking and disturbance rejection are given and l_1 and l∞ FSTS controllers are obtained using linear programming optimisation.