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In the last twenty some years, much attention has been paid to the problem of fault-tolerant control in satellite attitude control systems and many methods have been developed and proven to be capable of tolerating certain types of system faults (see e.g., [1~5] and the references therein). However, these solutions focused mainly on keeping stability of the faulty systems and in less consideration of other performance indices. Actually, the performance requirements of practical satellite control systems are usually multi-objective even in faulty cases and it is desirable for fault tolerant systems to keep the required performance indices in a satisfactory and admissible region rather than the optimization of single index [6~7]. As is well known, in many practical applications, it is desirable to construct systems to achieve better transient property, strong anti-disturbance ability and adequate level of cost function performance. To this end, optimal controllers have been designed by assigning pole in a desired region (see e.g., [8] and [9]), using H∞ norm-bound constraint on disturbance attenuation [10, 11] and the guaranteed cost control (see [12] and [13]), respectively. Unfortunately, few results have been considered such performance indices simultaneously. Meanwhile, once some components of satellite attitude control systems go wrong, it is difficult to confirm desired multiple performances by the existing fault-tolerant control. Thus, it is necessary to investigate the problem of fault-tolerant control with multiple performance constraints. Therefore, it is our motivation to investigate the quadratic D stabilizable satisfactory faulttolerant control problem with consistent indices constraints for a class of satellite attitude control uncertain discrete-time systems subject to actuator failures. In view of possible actuator failure as well as uncertainties which do not satisfy matching conditions existing in both the state and control input matrices, we first derive the existence conditions of satisfactory fault-tolerant state-feedback control law. Then by LMI technique, a convex optimization problem is formulated to find the corresponding controller. The state-feedback controller is designed to guarantee the closed-loop system satisfying the pre-specified quadratic D stabilizability index, H∞ norm-bound constraint on disturbance attenuation and having the quadratic cost performance simultaneously, for all admissible value-bounded

Quadratic D Stabilizable Satisfactory Fault-tolerant Control with Constraints of Consistent Indices for Satellite Attitude Control Systems