Finite-Time $$H_\infty $$ Control for Time-Delayed Markovian Jump Nonlinear Systems with Parameter Uncertainties and Generally Uncertain Transition Rates

This paper mainly investigates the problem of finite-time \(H_{\infty }\) control for a class of uncertain Markovian jump nonlinear systems (MJNSs) with time-varying delay and generally uncertain transition rates. By constructing the appropriate Lyapunov–Krasovskii functional and free weighting matrices, a novel criterion on finite-time boundedness for the MJNSs with \(H_{\infty }\) performance is derived. We use a special way to deal with the bilinear terms, the mode-dependent state feedback controller is designed to ensure the \(H_{\infty }\) finite-time boundedness of the closed-loop system in the forms of strict linear matrix inequalities. Finally, numerical and practical examples are given to demonstrate the effectiveness of the proposed method.