A Jurdjevic-Quinn-type theorem for stochastic nonlinear control systems.

Mohamed Bensoubaya (1) , Abdelhak Ferfera (1) , Abderrahman Iggidr (1)

1 CONGE - Geometric control for non-linear systems

Considering the stochastic nonlinear control system dxₜ= f₀(x_t,u) dt +∑_j=1^p f_j(x_t,u) dW_t^j (x ∈ \bbfRⁿ, control u ∈ \bbfR^m, smooth coefficients f_j), the authors give Jurdjevic-Quinn type conditions for global asymptotic stabilization in probability by a feedback control u(x) not exceeding any prescribed bound. The feedback control is represented explicitely. The results generalize the stabilization theorem of Jurdjevic and Quinn for deterministic control systems that are linear with respect to the state and affine in the control as well as generalizations thereof to affine deterministic (Outbib and Sallet 1992) and stochastic (Florchinger 1994) control systems.

Mots clés: Lyapunov functions; La Salle's invariance principle; stochastic control system; stabilization by feedback; stability in probability; nonlinear control system; Jurdjevic-Quinn conditions; Stochastic nonlinear control systems; stochastic stability; state feedback law

Domaines: Systèmes dynamiques [math.DS]; Optimisation et contrôle [math.OC]; Automatique / Robotique

Mohamed Bensoubaya, Abdelhak Ferfera, Abderrahman Iggidr. A Jurdjevic-Quinn-type theorem for stochastic nonlinear control systems.. IEEE Transactions on Automatic Control, 2000, 45 (1), pp.93-98. ⟨10.1109/9.827361⟩. ⟨hal-01860798⟩