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Nonconservative LMI techniques for robust stabilisation of spatially interconnected systems

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.