Finite-Time Gain-Scheduled Control on Stochastic Bioreactor Systems with Partially Known Transition Jump Rates

In this paper, an observer-based finite-time continuous gain-scheduled control is designed for a class of stochastic bioreactor systems with partially known jump rates. By using gradient linearization approach, the nonlinear stochastic systems are described by a series of linear jump models at some selected working points, then based on stochastic Lyapunov–Krasovskii functional approach, a new robust stochastic finite-time stabilizable criterion is derived to ensure robust finite-time stabilization of the each jump linear system by means of linear matrix inequalities. This method is then extended to provide observer-based finite-time state feedback H∞ controllers for such linear jump systems. Lastly, continuous gain-scheduled approach is employed to design observer-based continuous H∞ controllers for the whole bioreactor jump systems. Simulation examples show the effectiveness and potential of the developed techniques