Sliding mode control of continuous-time weakly coupled linear systems with external disturbances

We investigate the problem of sliding mode control for continuous-time weakly coupled linear systems with external disturbances. This is the first study of sliding mode control for continuous-time weakly coupled systems. Using a decoupling transformation, a weakly coupled system is first internally decoupled into two subsystems that are weakly coupled through control inputs only. Then, two sliding mode surfaces are designed for each subsystem using two sliding mode control techniques. The presented procedure greatly simplifies design due to reduced dimensions of subsystems, while providing good approximate results with the accuracy of O(ϵ)O(ϵ), where ϵϵ is a small weak coupling parameter.