Advances in stabilisation of highly nonlinear hybrid delay systems

Hailing Dong, Xuerong Mao

Research output: Contribution to journalArticlepeer-review


Given an unstable highly nonlinear hybrid stochastic differential delay equation (SDDE, also known as an SDDE with Markovian switching), can we design a delay feedback control to make the controlled hybrid SDDE become exponentially stable? Recent work by Li and Mao in 2020 gave a positive answer when the delay in the given SDDE is a positive constant. It is also noted that in their paper the time lag in the feedback control is another constant. However, time delay in a real-world system is often a variable of time while it is difficult to implement the feedback control in practice if the time lag involved is a strict constant. Mathematically speaking, the stabilization problem becomes much harder if these delays are time-varying, in particular, if they are not differentiable. The aim of this paper is to tackle the stabilization problem under non-differentiable time delays. One more new feature in this paper is that the feedback control function used is bounded.
Original languageEnglish
Number of pages11
Publication statusAccepted/In press - 20 Oct 2021


  • Brownian motion
  • Markov chain
  • hybrid SDDE
  • bounded feedback control
  • exponential stability
  • Lyapunov functional

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