Reachable Set Estimation For Discrete-Time Systems With Time-Varying Delay And Disturbances

The problem of reachable set estimation has been an important research topic in control theory.In practical application,we usually require to find a bound of a set of all the states that are reachable from a given set.Therefore,determining the bound of reachable sets is of practical importance for the study of system performance.This paper is concerned with the problem of the reachable set estimation and statefeedback controller design for discrete-time systems and discrete-time systems with time-varying delay and bounded peak disturbances.The main work of this paper includes the following two aspects:In the first part,the problem of reachable set estimation for discrete-time system with bounded peak disturbance is introduced.The ellipsoidal bound of reachable set is obtained by constructing an appropriate Lyapunov functional.In addition,a state feedback controller is designed for discrete-time systems with control inputs,a sufficient condition for bounding the reachable set is obtained.Then,it is transformed into an optimization problem to obtain the minimum ellipsoid bound of the reachable set of the closed-loop system.In the second part,we study the discrete-time system with time-varying delay under bounded disturbances and control inputs.The initial condition of the system does not have to be zero.Based on the Lyapunov-Krasovskii functional approach,delay-dependent conditions for bounding the reachable set of the closed-loop system are derived by designing the state-feedback controller.These conditions guarantee the existence of an ellipsoid containing the state of closed-loop system under nonzero initial conditions.In order to make the ellipsoidal bound as small as possible,the minimum ellipsoid problem is transformed into an optimization problem with matrix inequality constraints.Numerical examples are given to illustrate the effective-ness of the obtained results.