Local non-quadratic H-infinity control for continuous-time Takagi-Sugeno models

LMI conditions for local stability and stabilization of continuous-time T-S fuzzy systems

“…x t ∈ L It is worth pointing out that polytopic bounds on each scalar MF have been employed in [11,39,41,45], and the use of bounds on the partial derivative of MFs was also pursued in [34][35][36][37][38], where absolute values of the partial derivatives of the MFs were bounded by some constants. For the stability analysis, it is necessary to introduce the following set of state variables:…”

“…Amongst the promising research topics, in this paper, we focus on the local stability approaches, which have turned out to be effective in improving the global approaches further [34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51]. Evaluation of the local stability is the problem of determining if there exists a neighborhood of the equilibrium point, called the domain of attraction (DA) [46], such that all trajectories of the system emanating from any initial point in the DA asymptotically converges to the equilibrium point.…”

“…The solution processes are formulated as single-parameter minimization problems subject to LMIs, which can be efficiently solved via a sequence of LMI optimizations such as a bisection algorithm or a line search process, or can be treated as eigenvalue problems (EVPs) [2] directly tractable via LMI solvers [3][4][5]. In comparison with existing results, the distinguished feature of the proposed methods is that while existing approaches [34][35][36][37][38][39]41] employ bounds on each scalar MF, a quadratic bound on the vector containing MFs is considered in this paper. Note that this quadratic bounding technique was also used in [40].…”

“…Recently, the problems of assessing the local stability, designing locally stabilizing control laws, and estimating the DA of T-S fuzzy systems have been addressed by many authors [34][35][36][37][38][39][40][41][42][43][44][45].…”

“…Research directions to reduce the conservatism include approaches searching for general classes of Lyapunov functions, such as piecewise Lyapunov functions [9,10], fuzzy Lyapunov functions (FLFs) [11][12][13][14][15][16], a class of Lyapunov functions using line-integral [17]; polynomial Lyapunov functions [18][19][20][21]; augmented FLFs [22][23][24]; methods using information on MFs' shape [25][26][27], Pólya's theorem [28][29][30][31][32][33]; and local stability approaches [34][35][36][37][38][39][40][41][42][43][44][45]. Amongst the promising research topics, in this paper, we focus on the local stability approaches, which have turned out to be effective in improving the global approaches further [34][35][36][37][38][39][40][41][42]…”