Design of $H∞$ Loop-Shaping Controller for LTI System With Input Saturation: Polytopic Gain Scheduled Approach

This paper demonstrates the design of $H∞$ loop-shaping controller for a linear time invariant (LTI) system with input saturation constraint. The design problem has been formulated in the four-block $H∞$ synthesis framework, which is equivalent to normalized coprime factor robust stabilization problem. The shaped plant is represented as a polytopic linear parameter varying (LPV) system while saturation nonlinearity is considered. For a polytopic model, the LTI $H∞$ loop-shaping controllers have been designed at each vertex of the polytope using linear matrix inequalities, and subsequently controllers are scheduled by adopting a certain interpolation procedure. The proposed controller ensures the stability and robust $L2$-performance of the closed-loop system due to vertex property of the polytopic LPV shaped plant. The effectiveness of the design method has been illustrated through a numerical example.