This paper investigates observer-based stabilization for nonlinear descriptor systems using a fuzzy integral sliding mode control approach. Observer-based integral sliding mode control strategies for the Takagi-Sugeno (T-S) fuzzy descriptor systems are developed. A two-step design approach is first developed to obtain the observer gains and coefficients in the switching function using linear matrix inequalities (LMIs), and the results are used to facilitate the development of a single-step design approach, which is seen to be convenient but introduces some conservatism in the design. The potential application to a class of mechanical systems is also considered. Since the descriptor system representation of mechanical systems is adopted, it is shown that in contrast to the existing fuzzy sliding mode control methods based on the normal system representation, the resulting T-S fuzzy system does not contain different input matrices for each local subsystem and the required number of fuzzy rules is consequently markedly reduced. Finally, the balancing problem of a pendulum on a car is numerically simulated to demonstrate the effectiveness of the proposed method.

This paper addresses the robust stabilization problem for T-S fuzzy stochastic descriptor systems using an integral sliding mode control paradigm. A classical integral sliding mode control scheme and a nonparallel distributed compensation (Non-PDC) integral sliding mode control scheme are presented. It is shown that two restrictive assumptions previously adopted developing sliding mode controllers for Takagi-Sugeno (T-S) fuzzy stochastic systems are not required with the proposed framework. A unified framework for sliding mode control of T-S fuzzy systems is formulated. The proposed Non-PDC integral sliding mode control scheme encompasses existing schemes when the previously imposed assumptions hold. Stability of the sliding motion is analyzed and the sliding mode controller is parameterized in terms of the solutions of a set of linear matrix inequalities which facilitates design. The methodology is applied to an inverted pendulum model to validate the effectiveness of the results presented.

This paper investigates the integral sliding mode control problem of T-S fuzzy interconnected descriptor system based on a reduced-order compensator. A canonical equivalent form for T-S fuzzy interconnected descriptor system is first introduced to facilitate the reduced-order compensator design. In terms of the measurable output variables of the T-S fuzzy interconnected descriptor system and the state variables of the proposed reduced-order compensator, an integral sliding mode control scheme is then developed for the T-S fuzzy interconnected descriptor system. The sliding motion is defined in the augmented space formed by the state variables of the original T-S fuzzy interconnected descriptor system and the resulting error system. It is shown that the designing parameters in the switching function can be simultaneously solved and the original T-S fuzzy interconnected descriptor system has no requirement to be relative degree one. Since the estimate error is bounded by an auxiliary dynamical system, when ideal sliding mode occurs, the resulting closed-loop system is asymptotically stable rather than uniformly ultimately bounded. Finally, a double-inverted pendulum system and a ball and beam system are numerically simulated to demonstrate the effectiveness and merits of the method proposed.

Linear switching function and integral-type switching function are two typical switching functions in the sliding mode control field. Based on these, this paper investigates the design problem of fuzzy descriptor sliding mode observers. Two canonical forms, which are the T-S fuzzy descriptor systems' counterparts of the canonical form in normal systems, are first proposed. In terms of the proposed canonical forms, a linear switching function-based fuzzy descriptor sliding mode observer and an integral-type switching function-based fuzzy descriptor sliding mode observer are designed, respectively. It is shown that although the linear switching function-based fuzzy descriptor sliding mode observer has a much simpler design structure than the integral-type switching function-based fuzzy descriptor sliding mode observer, the integral-type switching function-based design method can deal with a much larger range of T-S fuzzy descriptor systems than the linear switching function-based design method. Finally, three simulation examples are provided to verify the effectiveness and merits of the proposed method.

This paper deals with the problem of the fault detection (FD) for continuous-time singular switched linear systems with multiple time-varying delay. In this paper, the actuator fault is considered. Besides, the systems faults and unknown disturbances are assumed in known frequency domains. Some finite frequency performance indices are initially introduced to design the switched FD filters which ensure that the filtering augmented systems under switching signal with average dwell time are exponentially admissible and guarantee the fault input sensitivity and disturbance robustness. By developing generalised Kalman–Yakubovic–Popov lemma and using Parseval's theorem and Fourier transform, finite frequency delay-dependent sufficient conditions for the existence of such a filter which can guarantee the finite-frequency H₋ and H_∞ performance are derived and formulated in terms of linear matrix inequalities. Four examples are provided to illustrate the effectiveness of the proposed finite frequency method.

The purpose of this paper is to study the structure of quantum linear systems in terms of their Kalman canonical form, which was proposed in a recent paper. The spectral structure of quantum linear systems is explored, which indicates that a quantum linear system is both controllable and observable provided that it is Hurwitz stable. A new parameterization method for quantum linear systems is proposed. This parameterization is designed for the Kalman canonical form directly. Consequently, the parameters involved are in a blockwise form in correspondence with the blockwise structure of the Kalman canonical form. This parameter structure can be used to simplify various quantum control design problems. For example, necessary and sufficient conditions for the realization of quantum back-action evading (BAE) measurements are given in terms of these new parameters. Due to their blockwise nature, a small number of parameters are required for realizing quantum BAE measurements.