Local Stabilityanalysis And H∞Control Of Continuous-time Takagi-sugeno Fuzzy Model

Since the Takagi-Sugeno model was proposed, it has been studied in kinds ofresearch areas. For example, stability analysis, observer design, filtering design, delays,etc. The design of Lyapunov function plays an important role in those studies.Initially, a sufficient stability condition is obtained by applying the quadraticLyapunov function and the key of this condition is to find a common symmetric matrixwhich is really difficult to be found and will lead to its innate conservatism when thefuzzy system is very complex. In recent years, various of Lyapunov functions have beendesigned to reduce the conservatism of quadratic stability, such as piecewise Lyapunovfunction, fuzzy Lyapunov function and weighting dependent Lyapunov function.Recently, non-quadratic Lyapunov function has been designed according to thecharacteristics of discrete system. As this function contains more variables, morerelaxed conditions can be obtained. A new conclusion can be obtained if non-quadraticLyapunov function can be used in continuous system. But non-quadratic Lyapunovfunction contains membership functions. The derivative of membership functions mustbe dealt with in continuous system. This is a difficult problem to be solved.In this thesis, the non-quadratic Lyapunov function will be further explored forcontinuous-time T-S fuzzy system. Firstly, the non-quadratic Lyapunov function isdeveloped and local stability of continuous-time T-S fuzzy closed-loop system isanalyzed via new non-quadratic Lyapunov function and non-parallel distributedcompensation law. Besides, a detailed study of the derivative of membership functionsis conducted, different stable or stabilization region is obtained by limiting the systemstate in a region and changing the size of region boundaries. Secondly, a local H∞control new method is proposed to reject the disturbance for continuous-timeTakagi-Sugeno fuzzy model by applying the Lagrange multiplier method. Comparedwith the latest results in the literature, the merits of new method are two points:1，wecan get some LMIs to ensure the requirement that the local stabilization region shouldbe contained in C;2,we can find larger stabilization region than the latest results. In theend, two examples borrowed from the literature show the effectiveness of theconclusions.