Linear systems with single saturated input: stability analysis

The authors address the problem of the qualitative determination of the stability region for closed-loop systems with one bounded input. It is shown that the stability region form depends strongly on the number n_u of open-loop system eigenvalues with a positive real part. In particular, if the open-loop system is completely unstable (n_u=n) the stability region is bounded and diffeomorphic to the n-dimensional ball B ⁿ. Both from theoretical and practical viewpoints, the results provide a useful tool in understanding and designing saturated feedbacks