Interest in the area of state and parameter estimation in nonlinear systems has grown significantly in recent years. The use of sliding mode observers promises superior robustness characteristics that make them very attractive for noisy uncertain systems. In this thesis, a novel Time-Averaged Lypunov functional (TAL) is proposed that examines the effect of Gaussian noise on the stability of a sliding mode observer. The TAL averages the Lyapunov analysis over a small finite time interval, allowing for intuitive analysis of noises and disturbances affecting the system. Initially, a sliding mode observer for a linear system is analysed using the proposed functional. Later, the results are extended to various classes of nonlinear systems. The necessary and sufficient conditions for the existence of the observer are presented in the form of Linear Matrix Inequality (LMI), which can be explicitly solved offline using commercial LMI solvers. The types of nonlinearity examined are fairly general and embodies Lipschitz, bounded Jacobian, Sector bounded and Dissipative nonlinearities. All the system models considered are highly nonlinear and consist of system disturbances and sensor noise. The proposed sliding mode observer provides less conservative conditions to verify the existence and stability of the observer. The observer can also be effectively used for unknown parameter estimation as outlined in the final chapter of this report. Various examples are provided throughout the premise to support the proposed observer design and demonstrate its effectiveness.
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Thesis advisor: Vijayaraghavan, Krishna
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