Composite disturbance-observer-based output feedback control and passive control for Markovian jump systems with multiple disturbances

This study addresses the problems of the composite disturbance-observer-based (DOB) output feedback control and passive control for Markovian jump systems with non-linearity and multiple disturbances. The multiple disturbances include two kinds: one is supposed to be a norm-bounded vector; the other is described by an exogenous system with perturbations. The purpose of the problem addressed is to design a DOB output feedback controller such that (i) the resulting composite system is passive; and (ii) different types of the above disturbances can be attenuated and rejected, respectively. The characterisation of the gains of the desired disturbance observer and the matrices of the expected output feedback controller are derived based on the solution to a convex optimisation problem that can be easily solved by standard numerical software. Finally, a simulation example is employed to show the effectiveness of the composite control scheme proposed in this study.