New Stabilization of Continuous‐Time Delayed Systems Based on Partially Delay‐Dependent Controllers

Abstract

In this paper, a new approach is developed to discuss the stabilization problem for a class of continuous-time delayed systems, which is firstly achieved by a kind of partially delay-dependent controller. The main property of the desired controller is that both non-delay and delay states are contained. Different from the traditional stabilization methods realized by totally non-delay or delay state feedback controllers, both non-delay and delay states are contained but take place asynchronously, where the probability distributions of such terms are considered in the controller design process. Based on the established model, new stabilization conditions depending on such probabilities are presented with linear matrix inequality forms. Moreover, another general case in terms of probability having uncertainty is also considered. Finally, numerical examples are used to illustrate the effectiveness and superiority of the design methods.

Stability analysis of delayed Markovian jump systems with delay switching and state signals and applications

“…Due to page limit and the process similar to the former situation, the corresponding computed matrices are omitted here, where only the maximum allowable delay is given. In detail and similar to the above comparisons, one could get the maximum allowable delay based on Corollary 3 being , while based on References 41,42 is and smaller. Moreover, based on Lyapunov function (65), one could also get the maximum allowable delay .…”

“…By investigating the references as much as possible, it is found that no reference can be directly applied to the considered problems in this article. In order to make some possible and suitable comparisons and via considering lots of references, it could be known that the stabilization problem of system (44) via controller (52) can be made between Corollary 3 in this article and some references 41,42 . However, it is said that the key idea of partially delay‐dependent controllers in such two references cannot be applied and should be revised to be .…”

“…In other words, in order to design a common , positive definite matrix must be selected to be mode‐independent. Based on these explanations, it is computed from References 41,42 that where the control gain is computed to be Meanwhile, the maximum allowable disturbance is . Moreover, it can be said that Lyapunov function (64) for the system closed by …”

“…In order to make some possible and suitable comparisons and via considering lots of references, it could be known that the stabilization problem of system (44) via controller (52) can be made between Corollary 3 in this article and some references. 41,42 However, it is said that the key idea of partially delay-dependent controllers in such two references cannot be applied and should be revised to be u(t) = Kx(t − 𝜏). The main reason is that there is always a delay in switching signal 𝜂(t) and system state x(t) respectively.…”