Observer‐based controller synthesis for uncertain polynomial systems

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Abstract
The controller design for a polynomial system with uncertainties and some/all un‐measurable states is a hard issue for researchers. Furthermore, if there is no information for the upper bounds of uncertainties, the design work will be more challenging. In order to overcome these difficulties, this study proposes a novel approach based on the unknown input method and disturbance observer to synthesise an observer‐based controller for the mentioned system such that the states are estimated and stability of the system is achieved asymptotically. First, based on the unknown input method, let the uncertainties of the polynomial system be regarded as the disturbance, and then a new observer is proposed to estimate the disturbance and states simultaneously. Next, the observer‐based controller is synthesised with suitable parameters which are computed from the conditions in the main theorems. Those parameters are obtained by using Matlab tool to solve a set of polynomial linear matrix inequalities which are derived in the main theorems too. With the aid of Lyapunov theory and sum‐of‐square technique, the above two main theorems are derived. It is noted that this study allows the uncertainty bounds are unknown and some/all states are un‐measurable. Finally, two examples are presented to show the effectiveness of the proposed method.

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