Stability analysis and control synthesis for fuzzy-observer-based controller of nonlinear systems: a fuzzy-model-based control approach

• Published in: IET control theory & applications Vol. 7; no. 5; pp. 663 - 672
• Main Authors: Lam, Hak Keung, Li, Hongyi, Liu, Honghai
• Format: Journal Article
• Language: English
• Published: The Institution of Engineering and Technology 01.03.2013
• Subjects: bilinear matrix inequalities; control synthesis; control system synthesis; convex programming; feedback; feedback compensation; feedback loop; fuzzy control; fuzzy‐model‐based control approach; fuzzy‐observer‐based controller; global searching algorithm; linear matrix inequalities; Lyapunov method; Lyapunov methods; membership functions; membership‐function‐dependent stability analysis; nonlinear control systems; nonlinear systems; observers; search problems; solution‐searching algorithm; stability; system state estimation; Takagi–Sugeno fuzzy model; Takagi–Sugeno fuzzy model; fuzzy-observer-based controller; Lyapunov method; membership functions; feedback compensation; membership-function-dependent stability analysis; feedback; fuzzy control; feedback loop; bilinear matrix inequalities; linear matrix inequalities; system state estimation; fuzzy-model-based control approach; Takagi–Sugeno fuzzy model; search problems; stability; solution-searching algorithm; control synthesis; control system synthesis; convex programming; global searching algorithm; Takagi–Sugeno fuzzy model; nonlinear systems; nonlinear control systems; observers; Lyapunov methods
• ISSN: 1751-8644; 1751-8652
• DOI: 10.1049/iet-cta.2012.0465

This study proposes a new category of fuzzy-observer-based controllers to stabilise non-linear plants based on the fuzzy-model-based control approach. A fuzzy observer is proposed to estimate the system states of the non-linear plant and a fuzzy-observer-based controller using the estimated system states for feedback compensation is proposed to close the feedback loop for the control process. It does not require that the fuzzy observer and fuzzy-observer-based controller have to share the same premise membership functions and the same number of rules of the Takagi–Sugeno fuzzy model. A membership-function-dependent stability analysis approach is proposed to investigate the stability of the fuzzy-observer-based control system based on the Lyapunov method. A set of bilinear matrix inequalities (BMIs) is obtained to guarantee the system stability and control synthesis. To find a feasible solution of the BMI-based stability conditions, a solution-searching algorithm, which combines global searching algorithm and convex programming techniques, is proposed. A simulation example is provide to demonstrate its capability of relaxing control design flexibility and effectiveness.