Algebraic approaches for the design of simultaneous observers for linear systems

Gap Reduced Minimum Error Robust Simultaneous Estimation For Unstable Nano Air Vehicle

“…For plants that have the same number of inputs and outputs without common eigenvalues, the necessary and sufficient conditions for the existence of a simultaneous functional observer were presented in [10]. In [11], algebraic geometry tools were presented to characterize the simultaneous observability of a set of linear single-input single-output plants and also to design a simultaneous state observer for the same. The methods presented in [8]- [11] are not suitable for synthesizing a simultaneous estimator for a NAV due to the following reasons: All the plants of the NAV may be unstable and also can have zeros on the right half of the s-plane [12].…”

“…In [11], algebraic geometry tools were presented to characterize the simultaneous observability of a set of linear single-input single-output plants and also to design a simultaneous state observer for the same. The methods presented in [8]- [11] are not suitable for synthesizing a simultaneous estimator for a NAV due to the following reasons: All the plants of the NAV may be unstable and also can have zeros on the right half of the s-plane [12]. Also, the number of outputs of the NAV is more than the number of inputs violating the condition mentioned in [10].…”

“…Apart from this, the plants of the NAV are subjected to higher model uncertainties. In [8], [11], no method is explicitly proposed to provide the desired performance (to achieve the condition II) by the estimator when the plants are subjected to measurement noise and higher model uncertainties. To overcome the abovementioned limitations, one needs to develop a new method to synthesis a simultaneous estimator for a NAV.…”