Observer-based Sliding Mode Control for Semi-Markvoian Jumping Systems Driven by Fractional Brownian Motions*

This note concerns observer-based sliding mode control for uncertain delayed stochastic semi-Markovian jumping systems driven by fractional Brownian motion. A novel mode-independent sliding mode surface is constructed for the observer system, and a weighted matrix sum is introduced for the semi-Markovian jumping input matrices in the form of Kronecker product. Criteria on stochastic stability of the sliding surface synthesis are derived by using the Lyapunov function method and a new integral inequality. Observer-based sliding mode controller is designed for the reachability of the mode-independent sliding mode surface under semi-Markovian switchings. Lastly, a vertical taking-off and landing(VTOL) aircraft model is presented to verify our findings.