Control of linear systems subject to input constraints: a polynomial approach. I. SISO plants

A polynomial approach is pursued for locally stabilizing discrete-time linear systems subject to input constraints. Using the Youla-Kucera parametrization and the extended Farkas lemma, the problem of guaranteeing closed-loop stability for any initial condition chosen in a given polyhedron of the state-space is formulated as a linear programming feasibility problem. This paper, as the first of a series of two, collects introductory material and may be regarded as tutorial. For the sake of clarity, only SISO plants and stabilization in given polyhedral regions are considered.