Gain-scheduling control of LFT systems using parameter-dependent Lyapunov functions

An LFR approach to varying sampling control of LPV systems: Application to AUVs

“…However it is expected that these results, in particular their conservatism, might be improved considering improvements in LPV/LFR design, such as using new multipliers for Linear Fractional Transformations as in [15], or by using parameterdependent Lyapunov functions as in [16].…”

Fuzzy control turns 50: 10 years later

“…Although the assumption is understandable for stability results, when z ≡ x, which is the case in nonlinear systems modelled as TS ones, it is more questionable for stabilization as, by chain rule, dµi(x) dt = ∂µi ∂x Tẋ andẋ can contain the to-be-designed control action in a general case, so the validity region of the obtained controller must be checked a posteriori, see discussion in [67]. In [68], the parameter-dependent (a.k.a. fuzzy) Lyapunov function is exploited for stabilization with output-feedback gain-scheduled controller for linear-fractionaltransformation descriptions; the resulting controller needs real-time measurements of the parameters (memberships) and their derivative.…”

Direct identification of continuous-time LPV models

“…This LPV modeling concept allows for a wide representation capability of physical processes, but the real practical significance of the LPV framework lays in its well worked out and industrially reputed control synthesis approaches, e.g. [1], [18], [24], that have led to many successful applications of LPV control in practice [3], [13], [14], [23].…”