On necessary and sufficient conditions for finite-time control of positive stochastic Poisson jump systems

In this paper, we consider the stochastically finite-time L 2 control problem for a class of positive stochastic Poisson jump systems (PSPJSs). By introducing a novel mode decoupling technique, some necessary and sufficient conditions are given to guarantee the stochastic finite-time boundedness of the input-free PSPJSs. Then, a proper mode-dependent finite-time state feedback controller is designed such that the positiveness, stochastic finite-time boundedness and the specified L 2 disturbance attenuation performance are attained simultaneously for the closed-loop SPJSs. Finally, two examples are given to show the feasibility and validity of the proposed methods.