H∞ gain-scheduling control for 2-D stochastic nonlinear systems: The F-M case

This paper is concerned with the H_∞ control problem for two-dimensional (2-D) stochastic systems with randomly occurring nonlinearity. The randomly occurring nonlinearity is modeled by using a Bernoulli random variable with known occurrence probability, which can characterize the phenomenon that the nonlinear disturbance may occur in a probabilistic way. Our attention is focused on the design of a probability-dependent gain-scheduling controller such that both the globally asymptotical stability in the mean-square sense and the H_∞ performance of the closed-loop 2-D system can be simultaneously guaranteed. Instead of the rigid gains of the traditional controller, the structure of the constructed 2-D controller is of a special form which depends on the time-varying probability of the randomly occurrence nonlinearity. By constructing a energy-like quadratic function, sufficient conditions are established to ensure the desired performance requirements. The obtained matrix inequalities can be readily solved by using the Matlab Toolbox. Finally, an illustrative example is provided to show the feasibility and usefulness of the developed gain-scheduling control scheme.