On the controller synthesis for linear hybrid systems

This paper deals with the control of a class of perfectly modelled linear hybrid systems which consist of two, in general coupled, subsystems—one being continuous time while the second one is digital. Both subsystems are driven by continuous time and sampled values of a control input. The description of the overall system is given through an extended hybrid system, which is purely discrete at sampling instants, which has two, in general, coupled continuous‐time and discrete‐time substates. The discrete‐time substate is jointly defined by the digital substate and the samples of the continuous substate while being driven by the sampled input. The control objective has a double nature and it consists of the achievement of separate continuous‐time and discrete‐time model‐matching objectives with respect to two predefined stable reference models. It is achieved by synthesizing a dynamic hybrid controller consisting of a continuous subcontroller and a discrete one. Each of those controllers has its own control objective: namely, the achievement of closed‐loop model following on a prescribed continuous‐time or sampled‐time reference model. The discrete reference dynamics could potentially be run at slow sampling periods and used for periodic readjustment of the continuous one in terms of variations of high‐frequency gains, set points or inputs to the continuous reference model.