Disturbance decoupling and design of unknown input observers for hybrid systems with state-driven jumps

In this paper two classical problems of interest in control theory, namely disturbance decoupling and the design of Unknown Input Observers (UIO), are revisited in the context of linear hybrid systems in the presence of state-driven jumps, induced by multi-affine sets. Interestingly, the latter feature renders the overall problem intrinsically nonlinear, hence classical (geometric) conditions cannot be straightforwardly applied. Firstly, it is shown that the definition of the disturbance decoupling control objective needs to be adapted to the hybrid setting, by distinguishing between weak and strong decoupling. In the former, the desired requirement consists in ensuring that the output of the plant is independent of the disturbance on each flow subinterval and across the successive jump, while the latter requires that both the output trajectory and the corresponding time domain, which is potentially perturbed in the uncontrolled case, are not affected by the disturbance. Easily verifiable geometric necessary and sufficient conditions to achieve weak or strong decoupling are presented and discussed. Then, it is shown that the solution to an auxiliary strong decoupling control problem is instrumental for the design of unknown input observers, whose existence conditions mimic and extend those for purely continuous-time systems. The paper is concluded by numerical simulations that corroborate the theoretical analysis.