Sliding Mode Controller Design For T-S Fuzzy Descriptor Systems

Sliding mode control is an important method in robust control field.Its merits involve the tractability and the invariance to parameter uncertainties and external disturbances.After decades of development,sliding mode control theory of normal systems has been initially formulated.Although the sliding mode control problem of descriptor systems and T-S fuzzy systems has also received considerable attention,it has been recently shown that several crucial issues remain unsolved.As a result,it is still an important task to develop sliding mode control methods for descriptor systems and T-S fuzzy systems.Based on the previous work,this thesis further develops sliding mode control method for linear and T-S fuzzy descriptor systems.The main efforts will be focused on the estab-lishment of descriptor regular form,the development of systematic ways to design sliding mode controller and observer for linear descriptor systems,the design of fuzzy switching functions for T-S fuzzy descriptor systems and the observer-based sliding mode controller designs for both linear and T-S fuzzy descriptor systems.The notion of descriptor regu-lar form and fuzzy switching function are introduced.Systematic ways to design sliding mode controller/observer for linear descriptor system and approach to design fuzzy feed-back gain based integral-type switching function are presented.The main contributions of this thesis are summarized as follows:(1)The sliding mode controller and observer design problems of linear descriptor systems are investigated via the linear switching function.A descriptor regular form,which is the counterpart of the regular form,is first introduced in the linear switching function case.Based on the proposed descriptor regular form and high-order sliding mode control technique,systematic ways to design sliding mode controller and descriptor slid-ing mode observer for descriptor system are given.Finally,it shows that the resulting closed-loop system,which is composed of the plant,the sliding mode controller and the descriptor sliding mode observer,satisfies the separation principle.This means that the sliding mode controller and the descriptor sliding mode observer can be separably de-signed.(2)The sliding mode controller and observer design problems of linear descriptor systems are studied through the integral-type switching function.A descriptor regular form,which is another extension of regular form,is first established in the integral-type switching function case.Based on the proposed descriptor regular form and high-order sliding mode control technique,the reduced-order observer,descriptor sliding mode ob-server and observer-based sliding mode controller generated by them are designed in a systematic way.It shows that the resulting closed-loop system,which is composed of the plant,the sliding mode controller and the reduced-order observer/descriptor sliding mode observer,satisfies the separation principle.Finally,a brief discussion is given to show that the separation principle also holds for the resulting closed-loop system,which is composed of the plant,the sliding mode controller and the normal sliding mode observer.(3)The problem of fuzzy switching function design for T-S fuzzy descriptor sys-tems is addressed.Based on the descriptor regular form,a descriptor fuzzy regular form is defined.Then a linear switching function,a parallel distributed compensation(PDC)fuzzy and a non-parallel distributed compensation(Non-PDC)fuzzy switching function-based sliding mode control methods are developed,respectively.It shows that the lin-ear switching function-based method is the most tractable and the proposed Non-PDC fuzzy switching function-based method is less conservative.Finally,the fuzzy switching function-based sliding mode control method is formulated,which is the counterpart of the linear switching function-based sliding mode control method in linear descriptor systems.(4)The integral-type switching function design problem for Ito stochastic T-S fuzzy descriptor systems is studied.A linear,a PDC fuzzy and a Non-PDC fuzzy feedback gain-based integral-type switching functions are designed,respectively.It is shown that the linear feedback gain-based method facilitates the design and the Non-PDC fuzzy feed-back gain-based method reduces the conservatism of other methods.Finally,the fuzzy feedback gain-based integral sliding mode control method is formulated,which extends the integral sliding mode control method for linear descriptor systems.(5)The observer-based sliding mode controller design problem is investigated for T-S fuzzy descriptor systems with parameter uncertainties.Due to the presence of parameter uncertainties,the resulting closed-loop system does not satisfy separation principle.To this end,a single-step and a two-step design methods are respectively developed to obtain the designing parametric matrices.It shows that the single-step design method is more convenient in the design and the two-step design method is less conservative.Finally,the potential application to a class of mechanical systems is also considered.It shows that a T-S fuzzy descriptor system is not only a natural representation of this class of mechanical systems,but also facilitates the design.(6)The sliding mode controller design problem for T-S fuzzy interconnected descrip-tor systems is considered when the state variables are partially measurable.A decompo-sition form for the coefficient matrices of T-S fuzzy interconnected descriptor systems is introduced,which facilitates the separation of the measurable state variables and immea-surable state variables.In terms of the measurable state variables and the estimation of the immeasurable state variables,a sliding mode controller design method is proposed.This method can ensure the asymptotic stability of the resulting closed-loop system,thus,it improves the traditional output feedback sliding mode control method.