On maximizing the convergence rate for linear systems with input saturation

In this paper, we consider the problem of maximizing the convergence rate inside a given level set for both continuous-time and discrete-time systems with input saturation. We also provide simple methods for finding the largest ellipsoid of a given shape that can be made invariant with a saturated control. For the continuous-time case, the maximal convergence rate is achieved by a bang-bang type control with a simple switching scheme. Sub-optimal convergence rate can be achieved with saturated high-gain linear feedback. For the discrete-time case, the maximal convergence rate is achieved by a coupled saturated linear feedback.