Intermittent-Type Quantized Control Based Fixed-Time Stability of Switched Filippov Systems on Networks

In this paper, fixed-time and practical fixed-time control of switched Filippov systems on networks with nondifferential delays are studied. Firstly, by using the comparison principle and intermittent control interval method, intermittent fixed-time stability lemmas with unified exponential conditions are proposed. The estimation of the settling-time shows that the elasticity number in the control interval plays a vital role. In order to solve the unavailability of global information, without using the auxiliary timer function, intermittent practical fixed-time lemmas with unified exponential conditions are established, which can improve the related ones greatly. It is necessary to point out that the residual set is relevant to the constant parameters of the system. The constant parameters of the system can be used to get a needed attraction region. Based on newly established stability lemmas, the fixed-time control and practical fixed-time control of the addressed switched Filippov systems are achieved based on the designed intermittent-type quantized control strategies, which enables the quantized control to be performed in intermittent intervals. Some previous control strategies are improved. Finally, numerical examples and simulations are provided to verify the validity of the obtained results.
Note to Practitioners
—Intermittent control has become popular recently since it saves more costs and is more practical in engineering. As for the complex networks, it is not enough to use intermittent control only, but also to consider the bandwidth of signal transmission. So, how to enable the quantized control to be performed in intermittent intervals is an interesting question. In addition, the global information of many models is unidentifiable, practical fixed-time control will be more realistic. Is the residual set in practical fixed-time control relevant to the intermittent control interval? These questions puzzled the authors and prompted this study.