Input To State Stability Of Dicrete-time Nonlinear Systems

In reality,the control system is often affected by the interferences in the controlling process or the discrepancies in the measuring procedure,and the requires the system not only to keep stability,but also to have the so-called "ISS" characterization.The notion of input to state stability(ISS) is now recognized as a central concept in nonlinear systems analysis,has very important Theoretical and engineering background.In this paper ,the equivalence between the ISS property and several variations in the discrete-time system is mainly reascarched.Firstly,several important property of the trajectory in the discrete-time systemare dissussing;Secondly,using trajectory analysis and Lyapunov function, series of equivalence properties of ISS in the discrete-time system,all this equivalence conditions enrich the research of stability in the discrete-time system are given;Finally, the definition of iISS and ilSS - Lyapunov function are also listed in this paper.