Observer-based feedback control of interval-valued fuzzy singular system with time-varying delay and stochastic faults

There are countless applications of non-linear systems that incorporate delay and algebraic equations. Despite current improvements in control theory, stochastic actuator defects still pose challenges when it comes to these systems. Furthermore, when it is not possible to measure the states of the system, and when uncertainties affect the system under investigation, the problem becomes even more complex. This paper is concerned with fault-tolerant observer-based controller synthesis for non-linear delayed singular systems with uncertainties and stochastic actuator failures. On the basis of interval valued models, a new Lyapunov-Krasovskii functional is built to develop a less conservative criterion to ensure that the closed-loop system is admissible in the mean-square sense. In addition, as these matrices are coupled with multiple variables, finding the parametric matrices of the observer and controller in terms of the obtained condition is more complex and challenging. The proposed method employs the matrix inequality decoupling technique to resolve this issue. Eventually, simulations are carried out to demonstrate the applicability of the proposed method.