Finite-dimensional observer-based controller for linear 1-D heat equation: An LMI approach

R. Katz*, E. Fridman

*Corresponding author for this work

Research output: Contribution to journalConference articlepeer-review

2 Scopus citations


The objective of the present paper is finite-dimensional observer-based control of 1-D linear heat equation with constructive and easily implementable design conditions. We propose a modal decomposition approach in the cases of bounded observation and control operators (i.e, non-local sensing and actuation). The dimension of the controller 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. The observer and controller gains are found separately of each other. 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. Different from some existing qualitative methods, we prove that the LMIs are always feasible for large enough N leading to easily verifiable conditions. A numerical example demonstrates the efficiency of our method that gives non-conservative bounds on N and δ.

Original languageEnglish
Pages (from-to)7611-7616
Number of pages6
Issue number2
StatePublished - 2020
Event21st IFAC World Congress 2020 - Berlin, Germany
Duration: 12 Jul 202017 Jul 2020


FundersFunder number
Israel Science Foundation673/19
Tel Aviv University


    • Distributed parameter systems
    • Heat equation
    • Lyapunov method
    • Modal decomposition
    • Observer-based control


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