OPTIMAL CONTROL APPLICATIONS AND METHODS Optim. Control Appl. Meth. (2012) Published online in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/oca.2031 A framework of robust fault estimation observer design for continuous-time/discrete-time systems Ke Zhang 1 , Bin Jiang 1, * ,† , Vincent Cocquempot 2 and Huaguang Zhang 3,4 1 College of Automation Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China 2 LAGIS-CNRS-FRE 3303, Lille 1 University : Sciences and Technology, Villeneuve d’Ascq Cedex 59655, France 3 College of Information Science and Engineering, Northeastern University, Shenyang, Liaoning 110004, China 4 Key Laboratory of Integrated Automation of Process Industry (Northeastern University) of National Education Ministry, Shenyang, Liaoning 110004, China SUMMARY A design framework of the observer-based robust fault estimation for continuous-time/discrete-time systems is presented in this paper. Firstly, a multiconstrained fault estimation observer under the H 1 performance specification with the regional pole constraint is proposed to achieve robust fault estimation. Then, the existence conditions for both continuous-time/discrete-time systems are derived explicitly. Furthermore, by introducing slack variables, improved results on the multiconstrained fault estimation observer design are obtained such that different Lyapunov functions can be separately designed for each constraint. Finally, sim- ulation results of a vertical takeoff and landing aircraft are presented to illustrate our contributions. Copyright © 2012 John Wiley & Sons, Ltd. Received 25 July 2010; Revised 7 January 2012; Accepted 15 March 2012 KEY WORDS: fault diagnosis; fault estimation; continuous-time/discrete-time systems; linear matrix inequalities 1. INTRODUCTION Increased productivity requirements and stringent performance specification of engineering systems have motivated intensive investigations on the design of fault detection and isolation and fault toler- ant control algorithms [1–4]. Observer-based fault detection and isolation techniques have received considerable attention and have been successfully applied to practical systems. Residual generation approaches using observers have been widely used, where the difference between the system output and observer output is processed to form the so-called residuals. Fault detection and isolation is used to monitor the system and to determine the location of the fault. After that, fault estimation (FE) module will be activated to online determine the magnitude of the fault, which may be used for fault tolerant control. As for the issue of FE for continuous-time systems, fruitful results have been obtained during the past two decades. Common FE methods use adaptive observer [5–7] or sliding mode observer [8–11] and generally apply for minimum-phase systems, which is a restrictive condition. In [12,13], a proportional-integral observer was used under the constant fault assumption, but FE performance was not considered, and no general approach was given. Therefore, how to relax these restrictive conditions (minimum-phase systems and constant fault assumption) and give a systematic FE method is a meaningful research work, which motivates our study in this paper. *Correspondence to: Bin Jiang, College of Automation Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China. † E-mail: binjiang@nuaa.edu.cn Copyright © 2012 John Wiley & Sons, Ltd.