In practice,many dynamical systems cannot be represented by the class of linear time-invariant model since the dynamics of these systems is random with features,for instance,economic systems,solar thermal receiver systems and communication systems.Such class of dynamical systems can be adequately described by the class of Markovian jump systems.In the past twenty years,Markovian jump systems have been extensively studied.This paper mainly concerns the robust stabilization and guaranteed cost control for delta operator Markovian jump systems with time-varying delays.Our purpose is to design a state feedback controller,such that the resulting closed-loop system is stochastic asymptotically stable,and the cost function value is not more than a specified upper bound for all admissible uncertainties.According to Lyapunov theory and introducing some appropriate free-weighting matrices,sufficient con-dition for the existence of the controller have been investigated in terms of linear matrix inequalities(LMIs),and after that we also tried to use the Mincx Solver in LMI toolbox to solve the optimization problems.The numerical examples verify the feasibility of the methods.The main research contents in this article are roughly three parts:(1)For Markovian jump delta operator systems with time-varying delays and norm bounded uncertainties,we design a state feedback controller,which can make the closed-loop system stochastic is asymptotically stable in delta domain.(2)For Markovian jump delta operator systems with time-varying delays and linear fractional uncertainties,we design a state feedback controller,which can make the closed-loop system is stochastic asymptotically stable,and the upper bound of the cost function is as small as possible.(3)For Markovian jump delta operator system with time-varying delays and convex polytopic uncertainties,a state feedback controller is designed,such that the resulting closed-loop system is stochastic asymptotically stable,and the robust guaranteed cost function value is not more than a specified upper bound for all admissible convex polytopic uncertainties. |