Study On Stability And Feedback Control For2-D Discrete Time System Subject To State Saturation

During the study of control system, the phenomena of the nonlinear willinevitably appear in various industrial systems and may yield the instability of thecontrolled systems. Saturation, as a common nonlinear constraint, include actuatorsaturation, observer saturation and state saturation. Although some new results havebeen obtained for2-D discrete time systems subject to state saturation, but also isnot relatively perfect. Especially, there is few research when some other complicatedfactors exist in2-D discrete time systems, such as time delay and nested saturationand so on. In this paper, the problems of stability analysis and feedback control areinvestigated for a class of2-D discrete time systems subject to state saturation. It isexpected that a new stability criterion and feedback control approach are given for2-D discrete systems based on the Roesser model (R-model).Firstly, applying the improved convex domain method, the saturated function isproperly handled for2-D discrete time systems subject to state saturation. Using2-Ddiscrete Lyapunov function, a new stability condition of the system is given byintroducing non-negative scalar. The idea of auxiliary parameter structure is providedin the designing of state feedback control for2-D discrete time systems subject tostate saturation.Secondly, the memory state feedback control problem is investigated for a classof2-D discrete time delay systems described subject to state saturation by theRoesser model. The delays are allowed to be a bounded time-varying functions.Using2-D discrete Lyapunov-Krasovskii functional method, a sufficient condition ispresented to guarantee the global asymptotic stability of the closed-loop system byconstructing a nonnegative scalar which is considered the structural feature ofsymmetric positive definite matrix which is row diagonally dominant withnonnegative diagonal elements. Then, the design method of the memory statefeedback control and the numerical example are proposed. Finally, the problem of state feedback control is studied for state saturation2-Ddiscrete time delays system with nested actuator saturation based on the R-model.The saturation function is re-expressed by introducing state deviation matrix. Byintroducing the non-negative assistant scalars, the sufficient condition is proposed toguarantee the global asymptotic stability of the closed-loop system. Here, thepresented non-negative scalars are constructed by using symmetric positive definitematrix, which are row diagonally dominant with non-negative diagonal elements.Also, the design method of controller are presented for nested actuator saturation andthe numerical examples are given to show the effectiveness of the proposed stabilitycriterion. Then, the presented results are extended to the2-D discrete time systemsubject to state saturation with multilayer nested actuator saturation and more generalresult can be obtained.