Energy-based stabilisation and H robust stabilisation of stochastic non-linear systems

Yan Hong Liu, Gui Zhou Cao, Shu Xia Tang, Xiu Shan Cai, Jin Zhu Peng

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

This study proposes a constructive stabilisation and H robust controller design method for stochastic non-linear systems from a novel dissipation analysis and energy point of view. First, the authors propose a sufficient condition for the dissipation of stochastic Hamiltonian systems and discuss the energy property of the systems, which will be used for the stability analysis and feedback controller design. Then, the authors show that the system is (asymptotically) stable in probability if it is (strictly) dissipative. By completing the Hamiltonian realisation of the stochastic non-linear systems, a feedback controller is proposed to stabilise the system under the condition of dissipation and zero state detectability. For stochastic non-linear systems subjected to external disturbances, an energy-based H controller was proposed by choosing the Hamiltonian function to construct a solution of Hamiltonian-Jacobi inequality. Finally, the effectiveness of the proposed method was illustrated via the inverted pendulum systems.

Original languageEnglish
Pages (from-to)318-325
Number of pages8
JournalIET Control Theory and Applications
Volume12
Issue number2
DOIs
StatePublished - Jan 30 2018

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