A linear matrix inequality approach to parametric H∞ loop shaping control

The parametric H∞ loop shaping technique explores more design flexibility by introducing a free parameter that ensures robust stabilization with regard to normalized coprime factor uncertainty of the shaped plant. This paper addresses a design framework for parametric H∞ loop shaping control using linear matrix inequality (LMI) approach that provides a new set of solvability condition along with the larger feasibility region of solution space over the work of Gu et al. (1999) [6]. An equivalence between the Riccati equation based state-space approach and the proposed LMI framework is established and subsequently, an observer-based structure for parametric H∞ loop shaping controller has been realized. A numerical example is considered to demonstrate the effectiveness of the proposed method and the results therein are compared with the work of Gu et al. (1999) [6].