Discrete- Time Variable Structure Control for Casusal Nonminimum Phase Systems Using Stable System Center

Abstract

The output tracking is considered for discrete-time causal SISO n th order linear time invariant system with unstable zero dynamics (nonminimum phase zeros) via discrete-time variable structure control. The stable system center method that originally was developed for controlling the output in continuous time nonminimum phase causal system using sliding mode (variable structure) control is extended to the discrete-time systems. The developed discrete-time stable system center technique transforms an output tracking problem to a corresponding state variable tracking problem by asymptotically identifying the ideal internal dynamics for the unstable internal states of a discrete-time system. The causal disturbances and output tracking profiles are assumed to obey a linear exogenous system with known characteristic polynomial. The theoretical results are confirmed by robust to matched disturbances discrete variable structure control design for the track parabolic-type signal problem in the third order nonminimum phase systems