On relaxed LMI-based designs for fuzzy regulators and fuzzy observers

Conditions of output stabilization for nonlinear models in the Takagi–Sugeno's form

“…Of course the trivial solution would be for a fixed k: [13]. To outperform this result several ways are possible, for example using matrix properties [8,10,16]. Nevertheless, this way seems very hard in our case because it will introduce a huge number of additional variables which is not compatible with the actual LMI solvers.…”

“…Nevertheless, this way seems very hard in our case because it will introduce a huge number of additional variables which is not compatible with the actual LMI solvers. Let us quote that the application to these relaxations [8,10,16] is straightforward. As far as we know, the more interesting conditions implying no additional matrix can be found in [18].…”

A new fuzzy Lyapunov function approach for a Takagi–Sugeno fuzzy control system design

“…For the stability analysis of TS fuzzy control systems, many researchers have presented the conventional quadratic Lyapunov function approaches to find a constant positive definite matrix of a quadratic Lyapunov function satisfying the stability conditions of all subsystems [5,8,12,13,[15][16][17]19]. Recently, in order to find more relaxed stability conditions, a fuzzy Lyapunov function approach was introduced which utilized a fuzzy blending of multiple quadratic Lyapunov functions [6,[9][10][11].…”

Non-Fragile Dynamic Output Feedback Control Design for Fuzzy Stochastic Systems

“…(Remark 2) We employed the technique in [23] to relax the stabilizability conditions (4)- (7) for fuzzy systems. They can be further relaxed by other techniques(see [24], for example.). Taking the bounds of the time derivative membership functions in (8) into account, the proposed approach provides LMI conditions (4) and obviously generalizes the quadratic approach with V (x) =x T (t)ẼXx(t) whereX is a constant matrix.…”