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The extension of some of the results contained in Part I  to the case when only the plant outputs rather than all its state variables are accessible for measurement is discussed. A unified approach to the synthesis of an adaptive observer is presented whereby the plant state and parameters are simultaneously estimated. Uniform asymptotic stability of the scheme is proved using Lyapunov's direct method. The information provided by the adaptive observer is used to synthesize an adaptive controller for the plant. While all the principal results obtained here are for the case of a single-input single-output plant, extensions to special classes of multivariable systems is indicated.