Adaptive Observer Design for One-Sided Lipschitz Class of Nonlinear Systems | ||
| The Modares Journal of Electrical Engineering | ||
| Article 5, Volume 11, Issue 4, 2012, Pages 45-51 PDF (196.01 K) | ||
| Authors | ||
| Mohammad Karkhaneh1; Mahdi Pourgholi* 2 | ||
| 1M.s. Shahid Beheshti University | ||
| 2Department of Control Shahid Beheshti University | ||
| Abstract | ||
| This paper addresses adaptive observer design problem for joint estimation of the states and unknown parameters for a class of nonlinear systems which satisfying one-sided Lipschitz and quadratic inner bounded conditions. It’s shown that the stability of the proposed observer is related to finding solutions to a quadratic inequality consists of state and parameter errors. A coordinate transformation is used to reformulate this inequality as a linear matrix inequality (LMI). Sufficient conditions that ensure the existence of adaptive observer are expressed in forms of LMIs, which are easily tractable via standard software algorithms. If the proposed conditions are satisfied, then the state estimation errors are guaranteed to converge to zero asymptotically while, the convergence of the parameters is guaranteed when a persistence of excitation condition is held. The effectiveness of the proposed method is shown by simulation for the joint estimation of states and parameters of a numerical system. | ||
| Keywords | ||
| Adaptive observer; Nonlinear Systems; Nonlinear observers; One-sided Lipschitz; Linear matrix inequality | ||
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