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Stable and robust state feedback design for hybrid systems

We introduce methods for stable and robust controller design in hybrid systems. The first control strategy is based on state feedback of the hybrid plant. We show how such a hybrid controller should be designed in order to obtain stability and performance for the controlled system. This approach will not require the search for a Lyapunov function, since the design method guarantees the existence of a common quadratic Lyapunov function for the controlled hybrid system and therefore guarantees its stability. The second control strategy that we propose is based on the design of a single state feedback controller for a hybrid plant. If such a controller can be found it will guarantee stability and robustness. The design is based on a quadratic Lyapunov function. We calculate the stability interval of the controlled subsystems and this interval is used to construct the state feedback controller. The state feedback shifts the coefficients of the characteristic polynomial in such a way that they lie in the middle of the interval and will therefore be robust.