Robust stabilization of multi-parameter families of systems

We show that given any family of asymptotically stabilizable LTI systems depending continuously on a parameter that lies in a closed box of R^p, there exists a time-varying state feedback law v(t,x) (resp. a time-invariant feedback law v(x)) which robustly globally exponentially stabilizes (resp. which robustly stabilizes, not asymptotically) the family. Further, if these systems are obtained by linearizing some nonlinear systems, then v(t,x) locally exponentially stabilizes these nonlinear systems. Finally, v(t,x) globally exponentially stabilizes any time-varying system which switches “slowly enough” between the given LTI systems