Stability analysis of a proportional with intermittent integral control system

The stability analysis of a proportional with intermittent integral (PII) control system is presented. This PII control system utilizes a proportional controller to attenuate unpredictable disturbances with an intermittently invoked integral controller to cancel constant disturbances. The integral control action is replaced by a constant offset set to its final value allowing perfect tracking and rejection of constant signals. By this design, the proportional controller can be made more aggressive while maintaining stability margins and control actions at similar levels. Due to its control fashion, this PII control system is modeled as a switched system composed of both linear time invariant and linear time-varying subsystems. The stability of this switched system is analyzed using a multiple Lyapunov functions approach. Additional sufficient conditions to ensure stability for the PII controller parameters are derived.