Polytopic Invariance Analysis and Actuator Saturation for Linear System with Polytopic Uncertainty

A method for estimating the domain of attraction of the origin was presented for linear time-varying system under a saturated linear feedback. A simple condition is first derived in terms of an auxiliary control input sequence for determining if a given polytope is contractively invariant. This condition is shown to be less conservative than the existing conditions which are based on the linear criteria. For single input system, a polytope is made contractively invariant with unconstrained linear feedback law, then it is contractively invariant under the saturated linear feedback if and only if there exists a nonlinear feedback controller which makes the polytopic set contractively invariant