Quantisation effect on zero-order-holder discretisation of multi-input sliding-mode control systems

This study investigates the quantisation effect on dynamical behaviours of the zero-order-holder discretisation of multi-input sliding-mode control systems with matched uncertainties. The quasi-sliding mode induced by both quantisation and discretisation is analysed and the thicknesses of the boundary layers are calculated. It is shown that chattering phenomenon occurs in the union of the two boundary layers induced by both kinds of discontinuous laws. The stability condition is given and the authors show that the switching manifold has relatively low chattering frequencies due to quantised state feedback. Finally, the theoretical results are verified through the simulation study of a third-order system with two inputs.