Improved stability and stabilization criteria for multi-rate sampled-data control systems via novel delay-dependent states

This paper aims to obtain less conservative stability and stabilization conditions for sampled-data linear systems with multiple sampling rates. To this end, three novel delay-dependent states resulting from sampling are introduced in the augmented state, enabling the exploitation of the sawtooth-type characteristics of the sampling-induced delay in both stability and stabilization processes. Additionally, a novel discontinuous function is included in Lyapunov–Krasovskii-based functional to enhance the capacity to extract more information from specific sampling pattern for each state. Especially, to strengthen the interdependence among the components of the augmented state, supplementary zero equalities are incorporated into the stability analysis conditions. Furthermore, by including a novel weighted state derivative in the augmented state, this paper proposes an effective method that can transform the parameter-dependent stability conditions into stabilization conditions formulated in terms of linear matrix inequalities. Finally, the validity and practicality of the proposed method are demonstrated through two illustrative examples.