Observers And State-Feedback Controllers For Positive T-S Fuzzy Systems

Along with the wide application of fuzzy control technology, the stability and controllersdesign problems of general T-S fuzzy systems have been widely investigated by many researchersat home and abroad and many encouraging results have been obtained. However there exista class of varible which must be nonnegative in practical engineering. So the correspondingdynamic systems must be described by the positive T-S fuzzy systems. However, in recentyears, there is less research on positive T-S fuzzy systems. So based on the research status onthe T-S fuzzy systems and positive systems, this paper investigates the observers and state-feedback controllers design problems for positive T-S fuzzy systems. The main works of thispaper are given as follows:(1) The problem of designing positive observers for continuous-time positive T-S fuzzysystems with interval uncertainties is investigated. By using the Lyapunov stability theory, asufcient condition of the asymptotic stability for continuous-time positive T-S fuzzy systemsis given in terms of linear matrix inequalities. Then, based on the stability conclusion andconsidered the interval bounds of system matrices, a sufcient condition is obtained to guaranteethe existence of positive observers for continuous-time positive T-S fuzzy systems with intervaluncertainties. Based on this condition, the positive observers are designed. At last, a numericalexample is given to show the efectiveness of the proposed method by using LMI toolbox.(2) The problem of designing positive observers for discrete-time positive T-S fuzzy sys-tems with interval uncertainties is investigated. By using linear matrix inequalities theory andLyapunov stability theory, a sufcient condition of the asymptotic stability for discrete-timepositive T-S fuzzy systems is given. Then, based on the stability conclusion, applied Schurlemma and considered the interval bounds of system matrices, a method of designing positiveobservers for discrete-time positive T-S fuzzy systems with interval uncertainties is obtained. At last, a numerical example is given to show the efectiveness of the proposed method by usingLMI toolbox.(3)The problem of designing state-feedback controllers for continuous-time positive T-Sfuzzy systems is investigated. A sufcient condition of the asymptotic stability for continuous-time positive T-S fuzzy systems is given in terms of linear matrix inequalities. Then, based onthe stability conclusion, the state feedback controllers design method is given, which guaranteesthat the closed loop system is positive and asymptotically stable. At last, a numerical exampleis given to show the efectiveness of the proposed method by using LMI toolbox.