An improved stability criterion for linear systems with multi-rate sampled data

Abstract

This paper proposes a stability criterion for linear systems with multi-rate sampled data by constructing novel Lyapunov functionals. The systems are represented as linear systems with input delay. The Lyapunov functionals consist of a quadratic function, an integral term related to the sampling intervals of each sensor and looped-functionals related to the sampling intervals of whole systems. In the view of the Lyapunov stability theorem, the quadratic function and the integral term require the positivity condition, whereas the looped-functionals do not require the positivity condition because the functionals are zeros at the sampling instants. Furthermore, the looped-functionals exploit the information on the sampled state and the state at the next sampling instants. Based on the Lyapunov functionals, this paper derives a stability criterion in terms of linear matrix inequalities. The simulation results show the effectiveness of the proposed stability criterion.