Open AccessEnergy‐based stabilisation and H ∞ robust stabilisation of stochastic non‐linear systems
Author(s) -
Liu YanHong,
Cao GuiZhou,
Tang ShuXia,
Cai XiuShan,
Peng JinZhu
Publication year - 2018
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2017.0392
Subject(s) - control theory (sociology) , dissipation , hamiltonian system , dissipative system , hamiltonian (control theory) , inverted pendulum , linear system , mathematics , realisation , robust control , computer science , control system , mathematical optimization , nonlinear system , engineering , control (management) , physics , mathematical analysis , artificial intelligence , quantum mechanics , electrical engineering , thermodynamics
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.