Design of static loop shaping controller in four-block framework using LMI approach

This paper attempts to develop an alternate but simple technique for designing a static output feedback H ∞ loop shaping controller from four-block H ∞ framework. Sufficient conditions are established for the existence of a static H ∞ loop shaping controller. These conditions are in LMI form, and are different from those obtained in [Prempain, E. (2004). Static H ∞ loop shaping control. Control 2004. UK: University of Bath; Prempain, E., & Postlethwaite, I. (2004). Static H ∞ loop shaping control of fly-by-wire helicopter. In Conference on decision and control (pp. 1188–1195); Prempain, E., & Postlethwaite, I. (2005). Static H ∞ loop shaping control of fly-by-wire helicopter. Automatica, 41, 1517–1528] using normalized coprime factorization approach. Numerical examples are considered to illustrate the results of this paper.