Improvements on Non-quadratic Stabilization of Takagi-Sugeno Models via Line-Integral Lyapunov Functions

Non-quadratic stabilization of second order continuous Takagi-Sugeno descriptor systems via line-integral Lyapunov function

“…From [24], it is known that for a 2nd-order case, the Lyapunov function is path independent if and only if ( )…”

“…In order to avoid the time-derivatives of the MFs, the line-integral approach has been proposed for controller design, resulting in bilinear matrix inequalities (BMIs), which are no longer as efficiently solved as LMIs [14]. LMI constraints were found for the two-rule second-order case in [24].…”

“…This work proposes an approach for stability analysis and controller design based on the Finsler's lemma [25] and a line-integral Lyapunov function [14], [24]: it breaks the link between controller gains and the Lyapunov function; Moreover, it offers parameter-dependent LMI conditions instead of BMI constraints. The result for stabilization is guaranteed for the second-order case.…”

LMI conditions for non-quadratic stabilization of T-S models with pole placement assignation

“…According to path-independency conditions [20], [21], [22], LILF have the advantage to make the stability conditions free of the time derivatives of the membership functions. However, the stabilization results in [20] are given in terms of Bilinear Matrix Inequalities (BMI) and recent results have shown that LILF may lead to LMIs, but with a restriction to only second order systems [23], [24], [25]. Alternatively, Sum-Of-Square (SOS) approaches have been proposed but with a very restrictive modeling assumption on the system's input matrices [26], [27].…”

Some Refinements on Stability Analysis and Stabilization of Second Order T-S Models Using Line-Integral Lyapunov Functions

“…More recently, a less conservatism stabilization result has been proposed by Tognetti et al (2011) but through a two steps LMI algorithm. Moreover, the special case of a second order fuzzy model with two rules has been investigated for non-PDC controller design (Márquez et al, 2013), which complexity suggests how a generalization is challenging.…”