Finsler's relaxation for local H-infinity controller design of continuous-time Takagi-Sugeno models via non-quadratic Lyapunov functions

Improved scalar parameters approach to design robust H∞ filter for uncertain discrete-time linear systems

“…In the literature, there are several ways to find the optimal values of them [10,17,19]. In order to emphasize the improvement of scalar parameters approach in this paper, we still apply the tuning scalars algorithm in [19] to solve the optimal H ∞ filtering problem.…”

“…Afterwards, ideas on developing LMI relaxations and extra applications have been generalized via making full use of Finsler's Lemma [4,[8][9][10].…”

Local H ∞ controller design for continuous-time T-S fuzzy systems

“…In addition, the assumption of magnitudebounded disturbances was also used in [39,40]. Compared to [41], we add the continuity assumption of w(t) to improve rigorousness of the proof.…”

“…Among the promising results, in this paper, we focus on the local stability approaches. Recently, the local stability methods were extended to deal with the H ∞ control problems in [39,40] and to address the local stabilization problems with invariant set analysis subject to magnitude and energy-bounded disturbances in [41]. Especially, [41] developed LMI conditions to design controllers that ensure the state to be confined within the region where the T-S fuzzy model is defined when the magnitude-and energy-bounded disturbances exist.…”

More Relaxed Non‐Quadratic Stabilization Conditions Using Ts Open Loop System and Control Law Properties

“…In , the path‐following method is utilized to solve the non‐strict problem. In , a prefixed value belonging to a logarithmical spaced family such as μ ∈ {10 −6 , 10 −5 , … , 10 6 } is considered to avoid exhaustive line search. Beside these efforts, the scalar parameters are chosen heuristically in several literatures .…”