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• W3089241465 abstract "Abstract The objective of the present paper is finite-dimensional observer-based control of the 1-D linear heat equation with constructive and feasible design conditions. We propose a method which is applicable to boundary or non-local sensing together with non-local actuation, or to Dirichlet actuation with non-local sensing. We use a modal decomposition approach. The dimension of the controller, N 0 , is equal to the number of modes which decay slower than a given decay rate δ > 0 . The observer may have a larger dimension N ≥ N 0 . The observer and controller gains are found separately by solving N 0 × N 0 -dimensional Lyapunov inequalities. We suggest a direct Lyapunov approach to the full-order closed-loop system and provide linear matrix inequalities (LMIs) for finding N and the exponential decay rate of the closed-loop system. We prove that the LMIs are always feasible for large enough N . The proposed method is different from existing qualitative methods that do not give easily verifiable and efficient bounds on the observer-based controller dimension and the resulting closed-loop performance. Numerical examples demonstrate that our LMI conditions lead to non-conservative bounds on N and the resulting decay rate." @default.
• W3089241465 created "2020-10-01" @default.
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• W3089241465 date "2020-12-01" @default.
• W3089241465 modified "2023-10-12" @default.
• W3089241465 title "Constructive method for finite-dimensional observer-based control of 1-D parabolic PDEs" @default.
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• W3089241465 doi "https://doi.org/10.1016/j.automatica.2020.109285" @default.
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