Sampling-interval-dependent stability for sampled-data systems with state quantization

This paper is concerned with the stability of sampled-data systems with state quantization. A new piecewise differentiable Lyapunov functional is first constructed by fully utilizing information about sampling instants. This functional has two features: one is that it is of the second order in time t and of every term being dependent on time t explicitly and the other is that it is discontinuous and is only required to be definite positive at sampling instants. Then, on the basis of this piecewise differentiable Lyapunov functional, a sampling-interval-dependent exponential stability criterion is derived by applying the technique of a convex quadratic function with respect to the time t to check the negative definiteness for the derivative of the piecewise differentiable Lyapunov functional. In the case of no quantization, a new sampling-interval-dependent stability criterion is also obtained. It is shown that the new stability criterion is less conservative than some existing one in the literature. Finally, two examples are given to illustrate the effectiveness of the stability criterion.