Polynomial Methods and Convex Optimization for the Control of Input Constrained Systems

A polynomial approach is pursued for locally stabilizing discrete-time linear systems subject to input constraints. Using the Youla-Kucera parametrization and geometric properties of polyhedra and ellipsoids, the problem of simultaneously deriving a stabilizing controller and the corresponding stability region is cast into a standard LMI problem. The approach is illustrated by a numerical example underlining the use of powerful CACSD tools such as the Polynomial Toolbox, Lmitool or Simulink for Matlab. Keywords Input Constraints, Polynomial Approach, LMIs, CACSD 1 Introduction The problem of control constraints appears in most practical control systems. Due to technological and safety reasons, the actuators cannot drive an unlimited energy to the controlled plant. The presence of input bounds can be source of parasitic equilibrium points and limit cycles, or can even lead the closed-loop system to an unstable behavior. 1 LAAS-CNRS, 7 Avenue du Colonel Roche, 31 077 Toulouse, Cedex 4..