IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 18, NO. 1, JANUARY 2010 201 Fault Detection for a Class of Uncertain State-Feedback Control Systems Guang-Hong Yang, Senior Member, IEEE, and Heng Wang Abstract—This brief studies the problem of fault detection for a class of uncertain state-feedback tracking control systems with constant reference inputs and bounded disturbances. The consid- ered systems are modeled via multiple modes, namely, fault-free case and faulty cases. Actuator stuck faults, including outage cases, are considered. With the aid of the finite-frequency positive-real- ness approach, a new linear-matrix-inequality-based fault detec- tion method for control systems is obtained and applied to fault detection for flight control systems. An F-18 aircraft model is in- cluded in the simulation to illustrate the effectiveness of the pro- posed method. Index Terms—Fault detection, linear matrix inequality (LMI), linear systems, state feedback, tracking . I. INTRODUCTION I N ORDER to improve the safety and reliability of indus- trial processes, particularly for flight control systems, fault detection techniques of control systems have attracted more and more attention (see [1]–[6] for more information). A fault rep- resents any kind of malfunction in a plant that leads to unac- ceptable anomalies in the overall system behavior. Such a mal- function may occur due to component failures inside the main- frame of the process, sensors, and actuators [7]. The classical observer-based fault detection scheme is to construct an ob- server, which takes the input and output of a system and gen- erates a signal called residual. This signal is then processed to decide whether a fault has occurred in the system [8]–[11]. Recently, linear matrix inequality (LMI) techniques have been applied in fault detection area, e.g., in [12], faults are estimated by designing an filter. In [13]–[17], faults are detected by satisfying certain performance indices. In [18]–[21], the fault detection problem is formulated as an optimization problem in frequency domain. In these papers, actuator faults are denoted by nonzero terms that are added to input channels. These fault models are quite classical and can Manuscript received December 01, 2006; revised March 28, 2008. Man- uscript received in final form November 27, 2008. First published April 21, 2009; current version published December 23, 2009. Recommended by Associate Editor I. Fialho. This work was supported in part by the Funds for Creative Research Groups of China (60821063), the State Key Program of National Natural Science of China (Grant 60534010), National 973 Program of China (Grant 2009CB320604), the Funds of National Science of China (Grant 60674021), the 111 Project (B08015), the Funds of Ph.D. program of MOE, China (Grant 20060145019), and the National 863 Plan of China (2006AA12Z307, 2008AA0085). G.-H. Yang is with the College of Information Science and Engineering, Northeastern University, Shenyang 110004, China, and also with the Key Laboratory of Integrated Automation of Process Industry, Ministry of Education, Northeastern University, Shenyang 110004, China (e-mail: yang- guanghong@ise.neu.edu.cn; yang_guanghong@163.com). H. Wang is with the College of Electronic Information and Control Engi- neering, Beijing University of Technology, Beijing 100124, China (e-mail: wangheng@bjut.edu.cn; wangheng19801980@126.com). Digital Object Identifier 10.1109/TCST.2008.2010521 describe a large class of fault types. However, the magnitude of faults should be large enough such that they can be detected [11], [18]. Actuator stuck faults, particularly the outages of actuators, are not well investigated through these fault models. On the other hand, the output tracking problem has a long his- tory [22] and plays an important role in flight control area, e.g., in [23] and [24], aircraft speed and position are regulated along a desired path. In [25] and [26], reference-input tracking prob- lems for flight control systems with actuator faults are consid- ered. Meanwhile, there is also a rising interest in designing flight control systems that would achieve various reliability goals in the presence of sensor/actuator faults [25], [27], and fault de- tection plays an important role in reaching reliability goals. The main objective of fault detection for a flight control system is to generate an alarm whenever the aircraft gets damaged or has inoperable control surfaces. As a result, control surface fault de- tection is urgently required in the event of faults. This brief considers the fault detection problem for a class of uncertain state-feedback tracking control systems with con- stant reference inputs and bounded disturbances. Through sat- isfying certain performance indices, a weighting matrix is de- signed to generate a residual signal. The residual output is min- imized when the system is fault free, while it is maximized when the system gets faulty. Thus, faults can be detected whenever they occur by observing the residual signal. With the aid of the finite-frequency positive-realness approach proposed in [28], an iterative LMI-based approach to fault detection is proposed to obtain the optimal solution of the weighting matrix. It should be pointed that, with the fault detection approach proposed in this brief, actuator stuck faults, including outage cases, can be detected effectively, which is nontrivial in the fault detection lit- erature. This brief is organized as follows. Section 2 presents the design objectives of this brief. Section 3 illustrates the fault detection design approach in detail. Section 4 shows the effec- tiveness of our approach by a design example. Some concluding remarks are given in Section 5. Notation: For a matrix , denotes its transpose. de- notes the identity matrix with an appropriate dimension. For a symmetric matrix , and denote posi- tive (semi)definiteness and negative (semi)definiteness, respec- tively. The symbol within a matrix represents the symmetric entries. and denote the maximum and minimum singular values of the transfer matrix , re- spectively. II. PROBLEM FORMULATION Consider a linear uncertain time-invariant aircraft model with external disturbance described by (1) 1063-6536/$26.00 © 2009 IEEE Authorized licensed use limited to: BEIJING UNIVERSITY OF TECHNOLOGY. Downloaded on December 30, 2009 at 20:28 from IEEE Xplore. Restrictions apply.