Finite L 2 gain and internal stabilisation of linear systems subject to actuator and sensor saturations

This study addresses the control of linear systems subject to both sensor and actuator saturations and additive ℒ2-bounded disturbances. Supposing that only the output of the linear plant is measurable, the synthesis of stabilising output feedback dynamic controllers, allowing to ensure the internal closed-loop stability and the finite ℒ2-gain stabilisation, is considered. In this case, it is shown that the closed-loop system presents a nested saturation term. Therefore, based on the use of some modified sector conditions and appropriate variable changes, synthesis conditions in a ‘quasi’- linear matrix inequality (LMI) form are stated in both regional (local) as well as global stability contexts. Different LMI-based optimisation problems for computing a controller in order to maximise the disturbance tolerance, the disturbance rejection or the region of stability of the closed-loop system are proposed.

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