Study On The Stability Of Uncertain Generalized Stochastic Systems

In the singular system, there are many papers are mainly studied for fixed time delay and segmented time delay. For the time delay of singular systems, there are many theories about fixed delay and segmented delay. Few people have studied singular systems witn randomly occurring delays. time delay and uncertainty parameters, which are affecting the good performance and stability of singular systems, exist in the practical application of the system. On the other hand, in the industrial production, because of the faults, the external environment of the mutation parts and other reasons, the structure and parameters of the system are often lead to jumpping phenomenon. Markov jump systems effectively describe this phenomenon. Thus, the stability study on uncertain singular systems and singular Markovian jump systems is important both in theory and in practice.Meanwhile, in practical engineering applications, control system components(such as actuators, sensors, etc.) that due to abrasion or aging inevitably fail, which will not only affect the control performance of the system, and even lead to the system be unstable. In this paper, with using of LMIs and established a Lyapunov function, we will study for the stability of the uncertain singular systems with randomly occurring time-varying delay and actuator faults. The main content of this thesis can be presented as two parts:In the first part, the study focused on the stability of uncertain singular systems with randomly occurring time-varying delay. With the constructed Lyapunov functional, a sufficient condition is given to ensure this kind of singular system to be mean-square exponentially stable. Then, we will design the state feedback controller to ensure that the system can reach steady state after failures. Finally, Some numerical examples have been provided to illustrate the effectiveness of results.In the second part, uncertain singular systems with randomly occurring time-varying delay with Markovian jump parameters have been researched. Established the model of the uncertain singular Markov jump system, with linear matrix inequality, a sufficient condition is given to ensure this kind of singular system to be mean-square exponentially stable. Then, to design the state feedback controller to ensure that the system can reach steady state after failures. Finally, some numerical examples have been provided to illustrate the effectiveness of results.