Parametrized linear matrix inequalities for nonlinear discrete H ∞ control

A new approach based on parametrized linear matrix inequalities (PLMIs) for solving nonlinear discrete H_∞ control is proposed. The “curse of dimensionality” is one of the main obstacles preventing nonlinear H_∞ control theory to be used in practice. However, in most applications, nonlinearity of a nonlinear system is caused by a few variables with dimension much lower than the plant dimension. Considering such nonlinear variables as parameters, the system can be handled as a family of linear systems depending on parameters in a reduced-dimension space. Then, PLMI tools can be used to render the nonlinear H_∞ control problem computationally tractable. Moreover, this approach can work well for output feedback problem giving a finitely dimensional control instead of a customized infinitely dimensional one