Computation algorithms of feasible sets and robust feasible sets for constrained linear time-invariant systems parametrized with orthonormal functions

Feasible sets and robust feasible sets have indispensable role in a priori stability guarantee of the constrained systems and in model predictive control. This article presents two algorithms for generating these sets for constrained linear time-invariant systems. Because the conventional algorithms for generating these sets must be applied iteratively over time, they are incapable of dealing with systems having the input vector constructed in any domain other than the time domain. The new algorithms, presented in this article, remove this limitation by treating the input vector monolithically over the time horizon. The presented algorithm for computation of the robust feasible set is capable of incorporating disturbances as well as parametric uncertainties that can be formulated as polytopes. For the verification, the results of the proposed algorithms were compared with results of the conventional methods in a similar circumstance. Finally, examples are presented to compare the computation times of the proposed algorithms with the conventional ones and to illustrate the effect of input vector parametrization, employing orthonormal functions, on the feasible region and the robust feasible region. Results showed that the parametrization improved the feasible set and robust feasible set.