On the state observation and output feedback problems for nonlinear uncertain dynamic systems

In this paper, we examine the problems of state observation and state trajectory control by output feedback for the class of non-linear systems in [3,11]. We begin by modifying a known discontinuous variable structure type observer into a continuous type observer that guarantees the observation error is Globally Exponentially Stable (GES). We then modify a known discontinuous variable structure type output feedback controller into continuous type output feedback controller that forces the state to the origin in the GES sense. Specific time-varying bounds on the observation error and the state trajectory are also developed; revealing how the corresponding observer or control parameters can be adjusted to improve the system performance.