Stability Analysis And Controller Design Of T-S Fuzzy Control Systems

In practical engineering, the controlled object is often non-linear control system, and theenvironment is complex. With the continuous development of industry, people areincreasingly high requirements for the controlled systems. Because of the unknowndisturbance input, if we want to use a precise mathematical model to accurately describe thecomplex nonlinear system, which is very difficult or even impossible. Fuzzy control due to itsunique system description method as the solution of such problems has brought a newresearch ideas. T-S model fuzzy system has the advantages of arbitrary precisionapproximation to nonlinear systems, which has attracted the attention of the majority ofscholars. T-S model fuzzy control elevated to a new level of theory, based the T-S fuzzysystem control sector has also become the new research hot spot.This paper makes the T-S fuzzy systems as the main research object, while theuncertainty of the system is taken into account, based on Lyapunov stability theory, and usethe parallel distributed compensation method, linear matrix inequality technique, the newfuzzy Lyapunov function method, this paper researches about stability analysis and controllerdesign to the contained uncertain T-S fuzzy the continuous system; the contained uncertainT-S fuzzy continuous system D domain guaranteed cost control problem; the uncertainty T-Sfuzzy discrete system, the second disc guaranteed cost control problem.The main work of this paper includes the following aspects:Firstly，based on the new fuzzy Lyapunov function, the paper researches about thestability analysis and controller design for the contained uncertain T-S model fuzzy systems,gets the sufficient condition which keeps the system with zero input stable, and verifies thatthe conditions has greater relaxation than the commonly used Lyapunov function method.And it designs a controller of the fuzzy system in the form of linear matrix inequalities, themethod in the paper does not have to know the number of rules is activated at some point,while decomposes looking for a common matrix to looking for p matrix, which makes themethod more less conservative, and the method is verified by simulation, it is feasible.Secondly，the paper uses linear matrix inequalities approach for contained uncertain T-Sfuzzy systems, proposes a controllers which can meet the stability of the system, and makesthe system closed loop poles into the given quadratic matrix inequality region of the complexplane,and makes the performance indicators of the system have an upper bound. There is nottoo much research paper about the fuzzy systems with pole placement problem, the systemdynamic performance and guaranteed cost control combined with literature rarely seen inpapers, a combination of both to consider, and the method is verified by simulation, it is feasible.Then，this paper proposes a stable guaranteed cost controller design method for a class ofcontained norm uncertainty T-S fuzzy discrete systems, and guarantees the closed-loop systempole placement in the specified disk area, and makes the given quadratic performance indexmeet its upper bound, and the method is verified by simulation, it is feasible.Finally，this paper proposes a H controller design method for a class of uncertain T-Sfuzzy systems, in condition of keeping the system quadratic stability sufficient condition,Secondary stability of the system to meet the design H state feedback controller, and theclosed-loop poles of the system configuration to the specified disk area, and the method isverified by simulation, it is feasible.