A fuzzy-linear-model-based variable structure control for nonlinear discrete-time systems

A nonlinear discrete-time system in the presence of input disturbance and measurement noise is approximated by subsystems described by input/output pulse transfer functions subject to disturbance and measurement noise although the input disturbance and the measurement noise are unknown, they are modeled as known pulse transfer functions. The approximation error is represented by a linear time-invariant dynamic system, whose degree can be larger than that of corresponding subsystem. In a steady state of set-point tracking, an equivalent linear time-invariant dynamic system is achieved. Under an assumption that the inverse of the equivalent characteristic polynomial of a stable closed-loop system can be expressed as a finite-degree polynomial the trajectory for a set point tracking reaches the switching surface in a finite-time step that is independent of the magnitude of input disturbance or measurement noise. Because of the presence of inflow disturbance or measurement noise or uncertainty, a huge transient response occurs. In this situation, a switching control is employed to improve the system performance.