This paper focuses on the observer-based robust stabilization problem for a class of polynomial systems with norm-bounded time-varying uncertainties. The structural features of such systems guarantee the fulfilment of the separation principle between the reduced-order observer and the state feedback. The existence conditions of the observer-based robust stabilization controller are obtained by using Lyapunov stability theory. Furthermore, based on the polynomial sum of squares (SOS) theory, the above conditions are transformed into the corresponding SOS convex optimization constraints, for the avoidance of computing difficulties that exist widely in the control of non-linear systems. Finally, two numerical examples are given to illustrate the feasibility and effectiveness of the proposed approach.

This paper aims to investigate the nonreciprocity caused by orthogonal magnetic field (OMF) vertical to the light direction propagating in a polarization-maintaining fiber-optic gyro (PM-FOG). In orthogonal magnetic field, the nonreciprocal phase error (NPE) results from the small change of the propagation constants of the two opposite light waves propagating in the fiber coil. Even using a PM fiber coil, the pressure, twist and other imperfections will change the polarization state, which may lead to an instable drift in PM-FOGs. This phenomenon was observed in the 0°-coupling regime which is commonly used for PM-FOG systems. Theoretical analysis and experimental results show and confirm that the instability of the NPE can be evidently reduced by taking a double-45°-coupling scheme. In this case, the NPE appears to be linear to the OMF and can therefore be compensated via later processes.Index Terms-Orthogonal magnetic field, nonreciprocal phase error, polarization-maintaining fiber-optic gyros, polarization state, coupling angle I.

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