Sliding mode control of a class of uncertain coupled systems: application to base isolated structures

The problem of feedback stabilization is addressed for a class of uncertain nonlinear mechanical systems with n degrees and n_c<n control inputs. Each system of the class has the structure of two coupled subsystems with n_c and n_r degrees of freedom, respectively, n=n_c+n_r. A practical prototype of such systems is an uncertain base isolated structure with n degrees of freedom actively controlled via actuators applying forces to the base movement of n_c<n degrees of freedom. A variable structure feedback strategy is proposed, under appropriate assumptions on the system uncertainties, to guarantee the asymptotic stability of the overall system