Disordered Stabilization of Stochastic Delay Systems: The Disorder-Dependent Approach

Abstract EN

In this paper, a general stabilization problem of stochastic delay systems is realized by a disordered controller and studied by exploiting the disorder-dependent approach.

Different from the traditional results, the stabilizing controller here experiences a disorder between control gains and system states.

Firstly, the above disorder is described by the robust method, whose probability distribution is embodied by a Markov process with two modes.

Based on this description, a kind of disordered controller having special uncertainties and depending on a Markov process is proposed.

Then, by exploiting a disorder-dependent Lyapunov functional, two respective conditions for the existence of such a disordered controller are provided with LMIs.

Moreover, the presented results are further extended to a general case that the corresponding transition rate matrix of the disordered controller has uncertainties.

Finally, a numerical example is exploited to demonstrate the effectiveness and superiority of the proposed methods.