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On the state observation and output feedback problems for nonlinear uncertain dynamic systems. (English) Zbl 0752.93021
Summary: We examine the problems of state observation and state trajectory control by output feedback for the class of nonlinear systems in A. Steinberg and M. Corless [IEEE Trans. Autom. Control AC-30, 1025- 1027 (1985; Zbl 0565.93047)] and Y. H. Chen [Int. J. Syst. Sci. 21, No. 5, 803-814 (1990; Zbl 0717.93007)]. 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.

MSC:
93B35 Sensitivity (robustness)
93C10 Nonlinear systems in control theory
93C15 Control/observation systems governed by ordinary differential equations
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