Qingling Zhang

The problems of impulse controllability and impulse elimination are investigated based on sliding-mode control (SMC) for Takagi–Sugeno (T–S) fuzzy singular systems (FSSs) in this article. Necessary and sufficient conditions for T–S FSSs to be impulse controllable are obtained based on the rank of matrices of system equivalent form. The relationship between impulses and fuzzy membership functions is given. The linear switching function and SMC law are designed to be applied to the impulse elimination of T–S FSSs. The main contributions of this approach are to design an SMC law, which can not only effectively eliminate impulses of T–S FSSs but also make the system asymptotically stable and give the principle of SMC to eliminate the impulse. Finally, the proposed method is applied to three examples. Examples 1 and 3 are to illustrate that SMC can effectively eliminate impulses of T–S FSSs. Example 2 verifies the superiority of this method by comparing with proportional and derivative feedback control law.

This paper is concerned with the problem of sliding mode observer (SMO) design for T-S fuzzy descriptor systems with time-varying delay. Firstly, based on the restricted equivalent transformation (RET), a new restricted equivalent form (REF) of descriptor systems is proposed. Under the new REF, an integral-type sliding surface is constructed for the error system. Then, a sufficient condition is established in terms of linear matrix inequality (LMI) which guarantees the admissibility of the sliding mode dynamics. Furthermore, a RBF neural network based adaptive sliding mode control (SMC) strategy is adopted such that the reachability condition can be ensured. By utilizing RBF neural network to approximate the unknown nonlinearity, many restricted conditions which are required in most existing results about SMC for T-S fuzzy systems, can be removed. Finally, a simulation example is presented to show the effectiveness of our results.

This paper investigates the problem of sliding mode controller design for a class of T-S fuzzy singular systems (TSFSSs) with partly immeasurable premise variables. By analyzing the different cases of immeasurable premise variables, novel state-feedback, and static output-feedback-based sliding mode controllers design methods are first developed. The information of measurable premise variables in TSFSS is utilized to design the controllers. Attention is focused on solving the problem of sliding mode controllers design for TSFSS with immeasurable premise variables related to time and system states. Further, based on the new sliding mode control (SMC) methods, some new convex conditions for designing sliding mode controllers are proposed. It is shown that the proposed sliding mode controllers design approaches have the advantage over existing SMC methods to stabilize the TSFSS with immeasurable premise variables. Finally, two simulation results are given to verify the feasibility and effectiveness of the proposed methods.

This study introduces a problem of positive filter design for positive piecewise homogeneous Markovian jump Takagi–Sugeno (T–S) fuzzy systems. The difference between the existing achievements is that the considered transition rate of the positive Markovian jump system is time‐varying. This time‐varying nature is finite piecewise homogeneous. The time variation of the transition rate is characterised by two cases: stochastic variation and arbitrary variation. First of all, sufficient conditions are obtained for stochastic stability and performance under the transition rate in a manner of stochastic variation and arbitrary variation by means of choosing a linear co‐positive Lyapunov function. Then, based on the obtained achievements, the problem of positive filter design for the positive piecewise homogeneous Markovian jump T–S fuzzy system is studied. All the mentioned problems in this study can be solved by linear programming. Finally, a biological model is proposed to illustrate the effectiveness of theoretical results.