The disturbance decoupling problem for hybrid systems with state-driven jumps

In this paper the problem of disturbance decoupling is tackled for linear hybrid systems in the presence of state-driven jumps, induced by multi-affine sets. Firstly it is shown that the definition of the control objective needs to be adapted to the hybrid setting, by distinguishing between weak and strong disturbance decoupling. In the former, the desired requirement consists in ensuring that the output of the plant is independent of the disturbance on each flowing subinterval followed by a single jump, while the latter requires that both the output trajectory and the corresponding, possibly perturbed, time domain are not affected by the disturbance. Then, easily verifiable geometric necessary and sufficient conditions to achieve weak or strong decoupling are presented and discussed. The paper is concluded by numerical simulations that corroborate the theoretical analysis.