Stabilization of networked control systems via non-monotone control ^lyapunov functions

This paper deals with stabilization of networked control systems (NCS) affected by uncertain time-varying delays and data packet dropouts. We point out that such network effects are likely to render the classical control Lyapunov function (CLF) method unfeasible, mainly due to the monotonic decreasing condition. To solve this problem we make use of a discrete-time equivalent of a control Lyapunov-Razumikhin function (CLRF), which is allowed to be non-monotone. The corresponding stabilizing control law is obtained by solving an optimization problem on-line, in a receding horizon manner, which incorporates the available knowledge about the past state/input trajectory. Furthermore, we provide extra flexibility to the CLRF via a relaxation variable, which is needed to handle hard state/input constraints. We also propose an effective method for dealing with delays larger than the sampling period by means of an on-line Minkowski set addition. This makes it possible to guarantee stability even in the presence of data packet dropouts, under certain assumptions.