Nonconservative LMI techniques for robust stabilisation of spatially interconnected systems

Xiaokai Zhai and Huiling Xu

International Journal of Systems Science, 2021, vol. 52, issue 1, 126-140

Abstract: This paper is concerned with the robust stabilisation problem of spatially interconnected systems (SISs) with linear fractional transformation (LFT) representation of uncertainties. A robust stabilisability function for SISs is built with the aid of Routh–Hurwitz criterion. By solving two semidefinite programs (SDPs) with sums-of-squares (SOS) polynomial constraints, necessary and sufficient conditions for establishing the existence of robust stabilising controllers are derived, implying that the derived robust stabilisation results are nonconservative. Moreover, a numerically tractable algorithm is proposed to obtain square matrix representation (SMR) of real polynomials, which enables the SOS constraints to be equivalently checked via linear matrix inequalities (LMIs). A simulation example is finally included to demonstrate the efficiency of the proposed method.

Date: 2021
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DOI: 10.1080/00207721.2020.1820623

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