Piecewise-linear robust control of systems with input constraints
The problem of robust local stabilization of an uncertain continuous-time system subject to input constraints is addressed. The nominal system is linear, and the uncertainty affects both the dynamic and the input matrices. The matrices describing the uncertainty are norm-bounded. No open loop stability assumptions are made. A set of initial conditions that can be stabilised and a robust control law are determined. Such a set of initial conditions is an ellipsoid, and the resulting control law is a piecewise linear state feedback, with switching boundaries defined as a nested family of positively invariant and contractive ellipsoids. Since the computations are performed off-line, solving a parametrised algebraic Riccati equation, or, alternatively, a parametrised linear matrix inequality related to a maximization problem, the main advantage of the proposed design algorithm is its simplicity, and the fact that it could be readily implemented.
scientific article; zbMATH DE number 1343411