Title :
Nonquadratic Stabilization of Continuous T–S Fuzzy Models: LMI Solution for a Local Approach
Author :
Pan, Jun-Tao ; Guerra, Thierry Marie ; Fei, Shu-min ; Jaadari, Abdelhafidh
Author_Institution :
Key Lab. of Meas. & Control of CSE, Southeast Univ., Nanjing, China
fDate :
6/1/2012 12:00:00 AM
Abstract :
This paper is concerned with nonquadratic stabilization design problem for continuous-time nonlinear models in the Takagi-Sugeno (T-S) form obtained by sector nonlinearity approach. Most of the previous results found in the literature intended to establish global nonquadratic stabilization conditions which are hard to uphold due to the difficulty of handling time derivatives of the membership function. By changing the paradigm of global stabilization for something less restrictive, a local solution to overcome infeasible quadratic stabilization conditions is offered in this paper. It is shown that the derived local nonquadratic conditions actually lead to reasonable advantages over the existing quadratic approach, as well as some previous nonquadratic attempts. Moreover, conditions for the solvability of state feedback controller design given here are written in the form of linear matrix inequalities (LMIs) which can be efficiently solved by convex optimization techniques. Simulation examples are given to demonstrate the validity and applicability of the proposed approaches.
Keywords :
continuous time systems; control system synthesis; convex programming; fuzzy systems; linear matrix inequalities; nonlinear control systems; stability; state feedback; LMI solution; Takagi-Sugeno form; continuous T-S fuzzy model; continuous-time nonlinear models; convex optimization; global stabilization; linear matrix inequalities; local approach; membership function; nonquadratic stabilization design problem; sector nonlinearity approach; solvability; state feedback controller design; Educational institutions; Fuzzy systems; Lyapunov methods; Stability analysis; Symmetric matrices; Trajectory; Vectors; Continuous-time Takagi–Sugeno (T–S) fuzzy models; linear matrix inequality (LMI); local stabilization condition; nonquadratic Lyapunov function (NQLF);
Journal_Title :
Fuzzy Systems, IEEE Transactions on
DOI :
10.1109/TFUZZ.2011.2179660