An exterior-point approach to the robust D-stability control problem

An iterative approach to the robust H<inf>&#x221E;</inf> synthesis problem with a sequence of infeasible controllers

“…Recently, various studies with parameter dependent Lyapunov functions have been reported to reduce the conservatism [2]- [4], [7], [9]- [14]. Especially, some interesting one-shot type approaches for designing robust H ∞ controllers using extended matrix inequality conditions have been proposed [12], [14].…”

“…From these facts, exteriorpoint approach is efficient for obtaining the solutions of the problems such that feasible solutions are difficult to be found. However, there are no exterior-point approaches except those in [6], [8], [9], [15] for control problems to our knowledge.…”

“…a common constant Lyapunov function for the entire uncertain set is used for reducing the infinite constraints to the finite ones at the expense of conservatism [1]. Recently, parameter dependent Lyapunov functions are used to overcome the drawback of the quadratic stability theory [2]- [4], [7], [9]- [14]. For the robust controller synthesis problems, some one-shot type approaches using extended LMI conditions, which allows to use the affine parameter dependent Lyapunov functions, have been proposed [12], [14].…”

An Iterative Approach to the Fixed-Order Robust H∞ Control Problem Using a Sequence of Infeasible Controllers

“…a common constant Lyapunov function for the entire uncertain set is used for reducing the infinite constraints to the finite ones at the expense of conservatism (Boyd et al 1994). Recently, parameter dependent Lyapunov functions are used to improve the conservatism (Chesi et al 2005) - (Ichihara et al 2003), (Kami et al 2009) - (Shaked 2001), (Xie 2008) and some one-shot type approaches using extended LMI conditions, which allows to use the affine parameter dependent Lyapunov functions, have been proposed (Pipeleers et al 2009), (Shaked 2001), (Xie 2008). However these methods can not always produce the robust controller, because common additional variables are required and these methods can not be used for designing fixed-order controllers.…”

“…From these facts, exterior-point approach can be efficient for obtaining the solutions of the problems such that feasible solutions are difficult to be found. However, there are no exterior-point approaches except those in (Iwasaki & Skelton 1995), (Kami & Nobuyama 2004), (Kami et al 2009), (Vanbierviet 2009) for control problems to our knowledge.…”