title: On the stability and control of continuous-time TSK fuzzy systems.
abstract: This paper introduces a new stability test and control design methodology for type-1 and type-2 continuous-time (CT) Takagi-Sugeno-Kang systems. Unlike methods based on a common Lyapunov function, our stability results apply for systems with unstable consequents, and our controllers can be designed for systems with unstabilizable consequents. The stability results are derived using the comparison principle with a discontinuous function and the upper right-hand derivative. The control results include CT fuzzy proportional controllers and fuzzy proportional-integral controllers that can be obtained by solving linear matrix inequalities. We provide several examples to demonstrate our stability testing and controller design and compare our results to available methods in the literature. Our results compare favorably with results available in the literature and provide stability tests and controllers where earlier approaches fail.
authors.affiliation: Department of Computer and Electrical Engineering and Computer Science, California State University Bakersfield, Bakersfield, CA 93311, USA. sjafarzadeh20@gmail.com
authors.forename: Saeed
authors.initials: S
authors.lastname: Jafarzadeh
authors.forename: M Sami
authors.initials: MS
authors.lastname: Fadali
mesh_terms: D000465:Algorithms; D001185:Artificial Intelligence; D005246:Feedback; D017143:Fuzzy Logic; D015233:Models, Statistical; D010363:Pattern Recognition, Automated / Q000379:methods*