On the stability analysis of sampled-data control systems: A combined continuous-time and discrete-time method

In this paper, we study the stability of sampled-data systems. A combined continuous-time and discrete-time approach is proposed, by adopting a switched system technique. Depending on the sampling period value, we treat the system as a switched system consisting of two subsystems. The two subsystems correspond to the small sampling case and the large sampling case, respectively. First, the small sampling case is studied by using the Razumikhin technique in the continuous-time framework. A condition is given to guarantee that the Lyapunov function decreases at the sampling instants, for the small sampling case. This Razumikhin-based result can be combined with the existing discrete-time methods so that the whole stability interval (small and large sampling parts) can be verified. This criterion is necessary and sufficient to guarantee the quadratic stability so that the maximum quadratic stability interval can be obtained. This combined continuous-time and discrete-time approach has two advantages over the existing approaches: 1) it can lead to a larger stability interval than those derived by the conventional continuous-time and discrete-time approaches; 2) it may reduce the computational complexity.