Energy-based stabilisation and H_∞ robust stabilisation of stochastic non-linear systems

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.