On the Solvability of Feedback Complete Linearization of Nonlinear Stochastic Systems

In this paper, solvability of the feedback complete linearization problem for single input nonlinear stochastic systems with multidimensional plant noise has been studied. Through a new theorem, necessary and sufficient conditions for the solvability of the problem are provided. The proposed theorem recognizes the existence of the diffeomorphism and feedback law for linearizing the nonlinear stochastic system without finding them. Checking the conditions of the proposed theorem in order to recognize the solvability of the feedback complete linearization problem, needs only simple matrices multiplication instead of complete solving the problem. The previous works need to solve a set of partial differential equations to recognize the solvability of the problem. The nonlinear stochastic systems that satisfy the conditions of the proposed theorem are completely linearizable, then linear stochastic control methods can be applied to control them and more accurate results in less computation will be achieved. Two numerical examples illustrate the theoretical results.