An impossibility result concerning bounded average-moment control of linear stochastic systems

Ahmet Cetinkaya, Masako Kishida

Research output: Contribution to journalConference articlepeer-review


It is known that strictly unstable linear systems that are subject to nonvanishing additive stochastic noise with unbounded supports cannot be stabilized by using deterministically bounded control inputs. In this paper, we explore similar impossibility results for scenarios where the expected value of the squared control input norm is subject to constraints and the support of the noise distribution is not necessarily unbounded. Specifically, we consider the stabilization problem with control policies that have bounded time-averaged second moments. We obtain values of such average second moment bounds, below which stabilization is not possible and the second moment of the state diverges regardless of the choice of the control policy and the initial state distribution. The results are illustrated with a numerical example.

Original languageEnglish
Pages (from-to)2267-2272
Number of pages6
Issue number2
Publication statusPublished - 2020
Externally publishedYes
Event21st IFAC World Congress 2020 - Berlin, Germany
Duration: 2020 Jul 122020 Jul 17


  • Constrained control
  • Instability analysis
  • Networked control
  • Stochastic systems

ASJC Scopus subject areas

  • Control and Systems Engineering


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