State predictive control with multiple modification terms and robust stability analysis based on complementary sensitivity functions

As an effective control method for systems with time delay in the input, state predictive control is well known. An idea of adding a single modification term to its control law was presented recently, and it was suggested that an appropriate modification term could contribute to improving robust stability of the control system to some parametric uncertainties. This extended control method is called modified state predictive control. Motivated by the preceding study, this paper considers introducing multiple modification terms into the control law of state predictive control, aiming at improving robust stability for non-parametric uncertainties. We first derive the characteristic equation of the modified state predictive control systems with multiple modification terms, and give a necessary and sufficient condition for stability. We then derive an explicit representation of the complementary sensitivity function associated with the robust stability analysis problem for multiplicative uncertainties. Finally, we demonstrate through numerical examples that state predictive control with appropriate multiple modification terms could be useful in improving robust stability compared with that with a single modification term or no such a term.