In this paper, the global asymptotic stabiliser design of rational systemsis studied in detail. To develop the idea, the state equations of the systemare transformed to a new coordinate via polynomial transformation and the state feedback control law. This in turn is followed by the satisfaction of the linear growth condition (i.e. Lipschitz at zero). Based on a linearmatrix inequality solution, the systemin the new coordinate is globally asymptotically stabilised and then, leading to the global asymptotic stabilisation of the primary system. The polynomial transformation coefficients are derived by solving the bilinear matrix inequality problem. To confirm the capability of this method, three examples are highlighted.

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