Adaptive integral sliding mode control with bounded ℒ2 gain performance of uncertain quantised control systems

Adaptive integral sliding mode control (ISMC) is investigated for a class of non-linear uncertain systems considering the mismatch relation between quantisation sensitivity parameters. First, by analysing the operation principle of the encoder/decoder, a mismatched relation between the quantisation parameters is established by using a time-varying ratio model, where the boundaries of the time-varying ratio can be unknown, regarding the existing cases as special ones. Second, using linear matrix inequality techniques, the prescribed bounded ℒ₂ gain performance condition is obtained for the sliding dynamics. Sequently, based on the formed boundary unknown time-varying ratio relation, adaptive ISMC laws are designed to ensure the reachability of the sliding manifold, then the establishment of the stability of the closed-loop system. Finally, an example is provided to illustrate the effectiveness of the proposed methods.