On the analysis of robust discrete time feedback control for nonlinear systems with parametric uncertainties

In this paper, a technique proposed by Paden et al. (1994) for analyzing the stability of nonlinear systems with parametric uncertainties under discrete time state feedback control is revisited and several new results are described. This technique was devised to study the stability of system with a control law designed to direct the system state near to a target manifold on which the system dynamics are stable. A method for greatly reducing the numerical difficulty associated with this technique is given. A theorem is presented that asserts that there exists a threshold sampling period such that effective digital robust feedback control can be achieved for a broad class of nonlinear systems, provided the sampling time chosen is less than or equal to this system dependent threshold value. In particular, this theorem assures that a control law can be chosen so that exponential stability of the closed loop system is assured and that there is a particular neighborhood of the target manifold which assures some degree of insensitivity of the closed loop system performance to the uncertain system parameters. An extension of this analysis technique to systems with certain disturbances is also given