ADDING INTEGRATIONS, SATURATED CONTROLS, AND STABILIZATION FOR FEEDFORWARD SYSTEMS

Our study relates to systems whose dynamics generalize x = h(y, u), y = f(y, u), where the state components x integrate functions of the oth er components y and the inputs u. We give sufficient conditions under which global asymptotic stabilizability of the y subsystem (respective ly, by saturated control) implies global asymptotic stabilizability of the overall system (respectively, by saturated control), It is obtain ed by constructing explicitly a control Lyapunov function and provides feedback laws with several degrees of freedom which can be exploited to tackle design constraints, Also, we study how appropriate changes o f coordinates allow us to extend its domain of application, Finally we show how the proposed approach serves as a basic tool to be used, in a recursive design, to deal with more complex systems, In particular t he stabilization problem of the so-called feedforward systems is solve d this way.