This paper proposes a novel kind of Unknown Input Observer (UIO) called Reset Unknown Input Observer (R-UIO) for state estimation of linear systems in the presence of disturbance using Linear Matrix Inequality (LMI) techniques. In R-UIO, the states of the observer are reset to the after-reset value based on an appropriate reset law in order to decrease the L 2 norm and settling time of estimation error. It is shown that the application of the reset theory to the UIOs in the LTI framework can significantly improve the transient response of the observer. Moreover, the devised approach can be applied to both SISO and MIMO systems. Furthermore, the stability and convergence analysis of the devised R-UIO is addressed. Finally, the efficiency of the proposed method is demonstrated by simulation results.

This paper proposes a novel kind of Unknown Input Observer (UIO) called Reset Unknown Input Observer (R-UIO) for state and fault estimation of a class of nonlinear uncertain systems using linear matrix inequality (LMI) techniques. In the devised R-UIO, the states of the observer are reset to the after-reset value based on an optimal H ∞ reset law in order to decrease the L 2 norm and settling time of estimation error. It is shown that the utilization of such an observer can significantly improve the transient response of the observer. Moreover, the devised approach can be applied to both SISO and MIMO systems. Furthermore, the robust stability analysis of the devised R-UIO is addressed. Finally, the capabilities of the proposed method are demonstrated by applying it to a Continuous Stirred-Tank Reactor (CSTR) as a practical model.

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Low-cost sensors based on micro-electro-mechanical systems (MEMS) are typically used for attitude determination in navigation systems especially magnetometer which is used for heading determination. The measured value of the MEMS magnetometer is subjected to different kinds of error such as random noise, constant bias, non-orthogonality, scale factor deviation and more importantly hard iron and soft iron effects. Therefore, in order to reach more accurate measurement, highprecision calibration is needed. One of the most common methods for calibrating MEMS magnetic sensors is least squares ellipsoid fitting. But, the common least squares ellipsoid fitting method can be inefficient for real-time applications in the presence of colored noise and outliers. In this paper, a modified ellipsoid fitting method is proposed in which a nonlinear optimization is developed to minimize a novel cost function. In the cost function of the proposed robust method, the effect of outliers and noise is considered and the standard deviation of the data is kept minimum. Finally, the efficiency of the new algorithms is demonstrated through the experimental results.

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