Sandwich control systems

In this letter, we combine the continuous systems with the impulsive control systems. Thus we propose a new mathematic model, namely sandwich control system. The system is a cyclic control system and there is no "rest time" for the inputs. The first and last parts of the system's inputs are continuous and other's is impulsive for a period of the system. We study the stability of it by constructing a Lyapunov function and using some mathematical techniques we get an exponential stability criteria in terms of a set of linear matrix inequalities. By the use of the results in this paper, the Chua's oscillor is controlled.