Multi-objective controller design for bi-linear stochastic systems via sliding mode control concept

A sliding mode controller u( t) is designed to achieve the following three objectives simultaneously: eigenvalue placement, H∞ norm constraint, and individual state variance constraint for bi-linear stochastic systems. By using the invariance property of sliding mode control, the matched bi-linear term of the system disappears on the sliding mode. With the aid of the upper bound covariance control theory, the controller u( t) is derived in which the control feedback gain matrix G is synthesized for achieving the above multiple objectives.