Stability and PID control of NCS with time-varying delay and packet dropout based on bi-feedback

For networked control system (NCS) with time-varying delay and packet dropout, new control methods, which are dynamical bi-feedback control and dynamical bi-feedback proportional-integral-derivative (PID) control, are proposed. The NCS with time-varying delay and data packet dropout based on four kinds of controller structures are modeled as four asynchronous dynamical systems (ADSs) constrained by event rates. According to the theory of ADS, Lyapunov stability theory and linear matrix inequality method, the semi-negative definite matrix conditions of exponential stability and design methods of dynamical bi-feedback controller and dynamical bi-feedback PID controller for the NCS with time-varying delay and packet dropout are presented. Furthermore, numerical examples are given to illustrate the feasibility of the semi-negative definite matrix conditions of exponential stability and controller design method.