Observer design for polynomial systems using convex optimization

This paper presents a computational technique of observer design for input-affine polynomial systems based on Lyapunov’s stability theorem and invariance principal by using convex optimization. Following some filter design results, an observer design method is discussed guaranteeing a regional stability of the closed-loop system for a given state estimate feedback law. Two performance improvements are also discussed with respect to the decay rate of the error dynamics, and the L
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gain between disturbances and the estimation errors. To compute these observer gains, scalar and matrix-valued sum of squares optimization are effectively used.