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The problems of delay-dependent robust stability and stabilisation for a class of uncertain two-dimensional (2-D) discrete systems with time-varying delays described by the second Fornasini-Marchesini local state space (FM LSS) model are investigated in this study. By employing improved free-weighting matrix approach, delay-dependent stability criterion for the nominal 2-D state-delayed system is first obtained and formulated in terms of linear matrix inequalities (LMIs); and then, a stabilisation design criterion using static state feedback controller is derived based on the stability result. Since the design criterion is not expressed strictly in terms of LMI, an improved cone complementary linearisation algorithm is employed to solve the non-convex feasibility problem. Furthermore, the stability and stabilisation results are extended to robust stability and stabilisation of the uncertain 2-D state-delayed system. Numerical examples are provided to demonstrate the effectiveness and advantage of the proposed method.