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Stabilisation of continuous-time switched 2D systems with all unstable modes

Stabilisation of continuous-time switched 2D systems with all unstable modes

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This study investigates the stabilisation of a class of continuous-time two-dimensional (2D) switched non-linear Roesser model with all modes unstable. Other than design controllers for the system, the authors would like to schedule the switching signal to achieve the asymptotical stability of the system. The main idea in this study is to utilise the alternative running of different subsystems to compensate the divergence of each subsystem, which thus achieves the stabilisation goal. By taking advantage of mode-dependent average dwell time property and a piecewise continuous Lyapunov function method, a general criterion is developed to guarantee the stability of the continuous-time switched 2D non-linear system with a designed switching law. The obtained result is further used to deal with switched 2D linear system. Finally, the effectiveness and superiority of the proposed methods are illustrated by two numerical examples.

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