Robust State-Estimator-Based Control of Uncertain Semi-Markovian Jump Systems Subject to Actuator Failures and Time-Varying Delay

This note presents a reformed state-estimator-based adaptive control strategy for uncertain delayed semi-Markovian jump systems (DSMJS) via sliding-mode technique. In comparison to most literature results requiring exact prior knowledge of system time delay, a linear state estimator not linking any control inputs is developed to cope with the case with unknown state delays. By virtue of the acquired state estimation, the establishment of both a new switching surface of linear-type (SSL) and the involved adaptive controller is provided, and the devised controller could not only admit the assigned SSL's reachability in limited time but also operate on the DSMJS as desired despite the hidden actuator failures and unknowable time delays. Also, a new sufficient stochastic stability criterion serving as a crucial solution to the control parameters of the resultant plant is inferred. The method also holds in a similar fashion for uncertain plants with no time delays and/or no switching case. Eventually, the raised method is verified by numerical examples.