Robust, fragile or optimal?

Abstract

In this paper we show by examples that optimum and robust controllers, designed by using the H2, H,, I' and p formulations, can produce extremely fragile controllers, in the sense that vanishingly small perturbations of the coefficients of the designed controller destabilize the closed loop control system. The examples show that this fragility also usually manifests itself as extremely poor gain and phase margins of the closed loop system.

Non-fragile observer-based H ∞ control for neutral stochastic hybrid systems with time-varying delay

“…Keel and Bhattacharyya [18] have shown by a number of engineering examples that the controller designed by using weighted H ? , l and l 1 synthesis techniques may be very sensitive, or fragile with respect to errors in the controller coefficients.…”

A Nonlinear Adaptive Resilient Observer Design for a Class of Lipschitz Systems Using LMI

“…In this work, a systematic algorithm is provided to check the feasibility of an asymptotically stable adaptive observer. An arbitrarily small disturbance may force the parameter estimates to drift toward infinity, while the state estimation error remains small [16,23]. Several techniques have been introduced to modify the adaptive observer structure to prevent parameter estimation drift.…”

“…Several techniques have been introduced to modify the adaptive observer structure to prevent parameter estimation drift. For instance, in [16] and [23], this goal has been achieved by designing robust adaptive observers assuming that the nonlinear terms only depend on the input and the measured outputs.…”

Delay-Dependent Nonfragile Robust H ∞ Filtering of T–S Fuzzy Time-Delay Systems

“…According to [8], those relatively small perturbations could destabilize the closed-loop system or the filtering error system, even if the perturbations are vanishingly small. Such controllers (filters) are often termed "fragile" or "nonresilient" controllers (filters).…”