Adaptive integral sliding mode control with bounded ℒ ₂ 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 ℒ 2 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.