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The problems of delaydependent robust stability and stabilisation for a class of uncertain twodimensional (2D) discrete systems with timevarying delays described by the second Fornasini–Marchesini local state space (FM LSS) model are investigated in this study. By employing improved freeweighting matrix approach, delaydependent stability criterion for the nominal 2D statedelayed 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 nonconvex feasibility problem. Furthermore, the stability and stabilisation results are extended to robust stability and stabilisation of the uncertain 2D statedelayed system. Numerical examples are provided to demonstrate the effectiveness and advantage of the proposed method.
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