| Full text | |
| Author(s): |
Gomes, Izabella O.
;
Tognetti, Eduardo S.
;
Oliveira, Ricardo C. L. F.
;
Peres, Pedro L. D.
;
IEEE
Total Authors: 5
|
| Document type: | Journal article |
| Source: | 2019 IEEE 58TH CONFERENCE ON DECISION AND CONTROL (CDC); v. N/A, p. 6-pg., 2019-01-01. |
| Abstract | |
This paper addresses the problem of nonquadratic stability and estimation of domains of attraction for continuous time nonlinear systems represented by Takagi-Sugeno (T-S) fuzzy models. The T-S fuzzy model is obtained by the sector nonlinearity approach and represents exactly the nonlinear system in a compact set of the state-space. Sufficient linear matrix inequality (LMI) conditions to access local stability are obtained using homogeneous polynomially parameter-dependent Lyapunov functions and slack variables introduced through the Finsler's Lemma. The time-derivatives of the membership functions are handled by means of a polytopic representation of the gradient of the membership functions. As a technical novelty, whenever possible, the nonlinear terms of the gradient are handled through a Taylor series expansion, avoiding the definition of new (generally overbounded) uncertain parameters that increase the numerical complexity. Finally, a numerical example is presented to show the superiority of the approach in terms of estimating larger domains of attraction when compared with previous methods from the literature. (AU) | |
| FAPESP's process: | 17/18785-5 - Parameter-Dependent Linear Matrix Inequalities Applied to Stability Analysis and Synthesis of Controllers and Filters for Uncertain Dynamic Systems |
| Grantee: | Pedro Luis Dias Peres |
| Support Opportunities: | Regular Research Grants |