Stabilization of linear systems with distributed infinite input delays: A low gain approach

Output feedback stabilization of Reaction-Diffusion PDEs with distributed input delay

“…To do so, let the error of estimation be defined by e n = z n − ẑn for 1 ≤ n ≤ N . Owing to (11a-11b) and invoking (7) and (10), we obtain that…”

Output feedback stabilization of linear time‐varying systems with infinite distributed input delays

“…Since systems with infinite distributed input delays always contain a part of the initial control function, their solutions are very sensitive to the initial condition. As a result, those works [28][29][30][31][32] all rely on this restrictive assumption on the initial control signal to obtain the stabilization results. (iii) Other general challenges in handling infinite delays also exist in this work, for instance, no delayed bound can be used to scale the integrals.…”

“…For instance, the authors in References 25‐27 utilize the extended Jensen's integral inequalities and Bessel–Laguerre integral inequality respectively to investigate stability problems of LTI systems with infinite distributed delays. The frequency domain low gain method is adopted to investigate stabilization problems 28,29 and an output regulation problem 30 of LTI systems with infinite distributed input delays, respectively. And this method is also employed by Zhou et al 31 to deal with the output feedback stabilization problem of LTI systems with both infinite distributed input and output delays.…”

Predictor feedback and integrator backstepping of linear systems with distributed unbounded delays

“…First, compared with most existing works where only bounded delays are considered, unbounded delays are discussed in this article. Second, compared with our previous works on systems with unbounded input delays, 44,45 this article considers systems with infinite-delayed integrators. It is shown that our stability theorems developed in Reference 46 can be applied to control problems of systems with infinite-delayed integrators.…”

“…It is shown that our stability theorems developed in Reference 46 can be applied to control problems of systems with infinite-delayed integrators. Last but not least, compared with our previous works where low gain approaches were applied, 44,45 this work considers more general linear systems with unbounded delays where open loop dynamics are allowed to be exponentially unstable, by designing a predictor feedback controller. Moreover, we have recently obtained some results on predictor feedback for infinite-delayed systems 51 where a new framework is developed, under which both time-invariant and time-varying linear systems with unbounded input delays can be dealt with.…”