Resilient dynamic controller design via quadratic Lyapunov bounds

One of the fundamental problems in feedback control design is the ability of the control system to maintain stability and performance in the face of system uncertainties. To this end, elegant multivariable robust control design frameworks such as ℋ_∞ control, L₁ control, and μ synthesis have been developed to address the robust stability and performance control problem. An implicit assumption inherent in these design frameworks is that the controller will be implemented exactly. In a paper by Keel and Bhattacharyya (1996) it was shown that even though such frameworks are robust with respect to system uncertainty, they are extremely fragile with respect to errors in the controller coefficients. In this paper, we extend the fixed-structure controller synthesis approach to develop non-fragile or resilient controllers to controller gain variations