Composite Anti-Disturbance Control of Hidden Semi-Markov Jump Systems via Disturbance Observer

This paper focuses on the disturbance suppression issue of hidden semi-Markov jump systems leveraging composite control. The system consists of a semi-Markov layer and an observed mode sequence layer, and it is subject to a matched disturbance generated by an exogenous system and a mismatched disturbance that is norm bounded. The proposal is to design a composite controller based on a disturbance observer to counteract and attenuate the disturbances effectively. By constructing a special Lyapunov function comparison point, the exponential stability is analyzed with the stability criterion in the form of linear matrix inequality is established. Two simulation examples are provided to demonstrate the practical merits of the composite controller relative to the single H_∞ control.