Finite-time H∞ control for continuous-time non-homogeneous semi-Markov jump systems

This article investigates the finite-time control problem for a class of non-homogeneous semi-Markov jump systems (SMJSs). First, since the time-varying transition rates (TRs) for jump rules between the system modes is taken into account, a new piecewise homogeneous approach is proposed to solve the nonhomogeneous phenomenon. Second, by resorting to Lyapunov theory, the state-feedback controller is designed and stochastic finite-time boundedness (SFTB) criteria with the prescribed $H_{\infty}$ performance level are established for the closed-loop SMJSs. Finally, an illustration are presented to verify the effectiveness of the proposed method.