Switched Observer Design for Reaction–Advection–Diffusion Systems: An LMI-SOS Approach with Adaptive Sensor Configuration

This paper addresses the state estimation problem for multivariable reaction–advection–diffusion systems governed by semilinear parabolic partial differential equations under switched sensor configurations. The spatial domain is partitioned into regions, each equipped with collocated sensors that can be selectively activated according to an output‐dependent switching law. The estimation error dynamics are formulated as a switched‐polytopic system, enabling the development of a systematic observer design methodology. Based on Lyapunov stability theory and polynomial parameterization techniques, sufficient conditions for exponential stability with guaranteed decay rate are derived in the form of linear matrix inequalities. These conditions are cast as sum‐of‐squares optimization problems, rendering them computationally tractable via standard semidefinite programming solvers such as SOSTOOLS and YALMIP. The proposed approach provides a constructive framework for synthesizing switched observers that optimize sensor utilization while maintaining estimation performance. A numerical example validates the effectiveness of the developed methodology, demonstrating significant improvements in convergence rate and computational efficiency compared to static observer designs.