Uncertain disturbances’ attenuation by homogeneous multi-input multi-output sliding mode control and its discretisation

Design of multi-input multi-output (MIMO) homogeneous sliding modes (HSMs) for uncertain dynamic systems is considered. The resulting closed-loop systems feature all well-known standard properties of single-input single-output (SISO) HSM systems. Introduction of robust exact differentiators produces homogeneous output-feedback controllers. The ultimate asymptotic accuracy of SISO HSM technique is proved to be preserved in the MIMO and SISO cases, if the discrete-time implementation is based on the one-step Euler integration.