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A switched equilibrium of a switched system of two subsystems is a such apoint where the vector fields of the two subsystems point strictly towards oneanother. Using the concept of stable convex combination that was developed byWicks-Peleties-DeCarlo (1998) for linear systems, Bolzern-Spinelli (2004)offered a design of a state feedback switching rule that is capable tostabilize an affine switched system to any switched equilibrium. The statefeedback switching rule of Bolzern-Spinelli gives a nonlinear (quadratic)switching threshold passing through the switched equilibrium. In this paper weprove that the switching threshold (i.e. the associated switching rule) can bechosen linear, if each of the subsystems of the switched system underconsideration are stable.

A linear state feedback switching rule for global stabilization of switched nonlinear systems about a nonequilibrium point