Stability Analysis And Design Of Discrete-time Singular System Subject To Actuator Saturation

Singular systems, which are also referred to descriptor systems, implicit system-s, have extensive applications in many practical systems such as engineering systems,social systems, economic systems, biological systems and so on. In the past severaldecades, the stability analysis and synthesis of linear singular systems have been exten-sively studied.In practice, most physical systems are subject to actuator saturation. The presenceof actuator saturation can lead to the performance degradation or even instability ofthe singular systems. Therefore, the analysis of singular systems subject to actuatorsaturation have received a lot of attentions.This thesis considered the stability analysis and design of the discrete-time singu-lar system subject to actuator saturation. The main results are listed as follows:First, the admissibility of the discrete-time singular system with actuator satura-tion is dealt with. A sufcient condition for the existence of a saturation avoidancefeedback controller is presented which guarantees the admissibility of the closed-loopdiscrete-time singular system. The largest constrictively invariant ellipsoid can be de-termined by solving an optimization problem. However, the information of initial stateis needed for this method.Second, the same discrete-time singular system is considered. A saturation al-lowance feedback approach is adopted to deal with the saturation of the control inputwhich is expressed in a form of convex by introducing an auxiliary matrix. As a result,a new criterion to stabilize the discrete-time singular system is derived. The obtainedresult removes the structural restriction on the feedback gain in the existing literature.In addition, we do not require the information of the initial state.Finally, we address the problem of a discrete-time singular system subject to ac-tuator saturation and nonlinear perturbation. The saturation allowance feedback controllaw is designed by use of the fixed point theorem to guarantee the regularity, causalityand stability of the system. In the same time, an optimization algorithm is proposed todetermine the largest constrictively invariant ellipsoid.