An-Yang Lu

Simultaneous fault detection and control for switched linear systems with mode-dependent average dwell-time

This paper investigates the problem of the simultaneous fault detection and control (SFDC) for switched linear systems. To meet the control and detection objectives, the time-dependent detection filters and dynamic output feedback controllers are presented in SFDC under a mixed H∞/ H - framework. A mode-dependent average dwell-time (MDADT) approach, which means that each subsystem has its own average dwell time, is adopted in this paper to reduce the conservativeness of the average dwell time method. And the discretized Lyapunov function (DLF) technique is first used to relax the MDADT constraints in SFDC. Some sufficient conditions for designing filters/controllers which satisfy the H∞/ H - performance are given in terms of linear matrix inequalities (LMIs). Whats more, a two-step algorithm to solve the SFDC problem is proposed. The effectiveness of the proposed method is illustrated through two simulation examples.

Fault detection for singular switched linear systems with multiple time-varying delay in finite frequency domain

ABSTRACT 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 Parsevals 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.

Dynamic output feedback H∞ control for switched T-S fuzzy systems via discretized Lyapunov function technique

This paper investigates the problem of the dynamic output feedback H ∞ control for a class of switched T-S fuzzy systems. Based on the mode-dependent average dwell time method and discretized Lyapunov function technique (DLF), a new method is proposed to analyze the stability for the switched fuzzy systems with unstable subsystems. In addition, by using the switched parallel distributed compensation scheme, a new membership-function-dependent switching law for the controllers is constructed. Then, the dynamic output feedback controller design for the switched systems with time-dependent switching law is proposed based on the DLF technique. Finally, sufficient conditions of the existence of the dynamic output feedback controller are proposed and formulated in the form of linear matrix inequalities (LMIs). The effectiveness of the proposed method is illustrated through three simulation examples.

Stability analysis and state feedback control of continuous-time T-S fuzzy systems via anew switched fuzzy Lyapunov function approach

This paper deals with stability analysis and control design problems for continuous-time Takagi-Sugeno (T-S) fuzzy systems. First, a new membership-function-dependent switching law is proposed and a relaxation parameter is introduced into this switching law to guarantee a minimal dwell time between two consecutive switching. Compared to the existing methods, the most important point is that with the help of the dwell time, the discretized Lyapunov function (DLF) technique can be adopted. Then a new stability criterion of the T-S fuzzy system with less conservatism is derived based on a fuzzy discretized Lyapunov function (FDLF). Second, to estimate the domain of attraction (DA), an algorithm with less iteration steps is proposed. Based on the proposed switching method, sufficient conditions for existence of the state feedback controllers are presented via the switched non-parallel distributed compensation (non-PDC) scheme. The effectiveness of the proposed method is illustrated through three simulation examples.

Asynchronous H∞ filtering for 2D discrete Markovian jump systems with sensor failure

This paper investigates the problem of the asynchronous H∞ filtering for a class of two-dimensional(2D) Markovian jump systems with sensor failure. The asynchronous phenomenon is considered to be random mismatch between system modes and candidate filters. The mismatch behavior is assumed to be stochastic with a certain probability and a new Markov chain is proposed to model the jumping process of the filtering error system. Besides, a switching method is proposed to dealing with the sensor failure. Sufficient conditions for the existence of a desired filter such that the filtering error system is stochastically stable with a guaranteed H∞ performance index are obtained in the form of linear matrix inequalities (LMIs). Two examples are provided to illustrate the effectiveness and advantage of the proposed method.

Event triggered H−/H∞ fault detection and isolation for T-S fuzzy systems with local nonlinear models

Abstract This paper is concerned with network-based fault detection and isolation(FDI) observer design for a class of Takagi–Sugeno (T-S) fuzzy systems with local nonlinear models. First, by combining the original system with the FDI observer, the closed-loop systems with asynchronous membership functions are modeled. Second, a new condition is introduced into the event-triggered scheme(ET scheme). This condition facilitates dealing with the asynchronous membership functions. Third, new relaxation terms are added to deal with the time delay disturbance and faults introduced by the Lyapunov–Krasovskii function(LKF) method. Then, sufficient conditions for the existence of the desired FDI observer which ensures the H − / H ∞ performance are proposed. Besides, a two-step algorithm is given to co-design the parameters of the ET scheme and a bank of observers are constructed such that each of them is sensitive to particular faults. An inverted pendulum example is given to illustrate the effectiveness of the new results.

Adaptive Fuzzy Tracking Control for a Class of Switched Uncertain Nonlinear Systems: An Adaptive State-Dependent Switching Law Method

This paper is concerned with the problem of adaptive fuzzy tracking control for a class of switched uncertain nonlinear systems. The unknown nonlinear functions are approximated by using fuzzy logic systems, and the adaptive backstepping technique is applied to a convex combination of the subsystems. To ensure the continuousness of the Lyapunov function at switching instants, common Lyapunov function (CLF) technique is adopted and the proposed CLF permits switched parameter adaptive laws. Besides, two classes of adaptive laws are proposed, one for designing control laws and one for designing switching law. Then, the common control laws are obtained with the help of the convex combination. Based on the switched adaptive laws, common control laws, a new adaptive state-dependent switching law is proposed. It is shown that the designed state-feedback controllers and switching law can ensure that all the signals remain bounded and the tracking error converges to a small neighborhood of the origin. Moreover, a modified switching law is proposed to avoid Zeno behavior or switching too quickly. Finally, two examples are provided to show the effectiveness of the proposed approaches.

Adaptive Tracking Control for a Class of Switched Nonlinear Systems Under Asynchronous Switching

This paper investigates the problem of adaptive fuzzy tracking control for a class of switched uncertain nonlinear systems under asynchronous switching. Inspired by the discretized Lyapunov function technique, a class of time-schedule Lyapunov functions (TSLFs) is first proposed to analyze the stability under asynchronous switching. Then, based on the proposed TSLF, novel observer and adaptive laws with time-schedule observer gain and design parameters are proposed to deal with asynchronous switching. Moreover, a switched command filter with the virtual control functions as input is proposed to avoid “the explosion of complexity” and tracking error jumps, which make the stability analysis difficult. It is shown that under the proposed controller, all the signals of the closed-loop system are bounded, and the tracking errors converge to a small neighborhood of zero in spite of asynchronous switching. Finally, the effectiveness of the proposed method is illustrated through two illustrative examples.

Network-based fuzzy H∞ controller design for T-S fuzzy systems via a new event-triggered communication scheme

Abstract This paper is concerned with network-based fuzzy H∞ control for a class of T-S fuzzy systems under an event-triggered communication scheme. Considering the fact that the network-induced delays are inevitable, the closed-loop system is modeled with asynchronous membership functions. To deal with the asynchronous membership functions, a new condition that limits the deviation bounds of membership functions, is introduced into the event-triggered scheme (ET scheme). Besides, by introducing a fuzzy event-triggered weighting matrix, a new ET scheme is proposed. Based on the proposed ET scheme, a novel criterion for the asymptotic stability and H∞ performance analysis is established in terms of linear matrix inequalities. Then some sufficient conditions and an algorithm to co-design the controller and the parameters of the ET scheme are presented. The effectiveness of the proposed method is illustrated through a mass-spring-damper system.