Observer-based periodically intermittent control for linear systems via piecewise Lyapunov function method

• The description of an observer-based periodically intermittent controller is first proposed.
• Piecewise Lyapunov function is constructed to analyze the stability of periodically intermittent control system, which results in the less conservative conditions.
• Compared with an observer-based continuous controller, the designed observer-based periodically intermittent controller can retain satisfactory effects with shorter control task execution time.

This paper focuses on the observer-based periodically intermittent control issue for linear systems by utilizing piecewise Lyapunov function method. Based on the concept of intermittent control, the description of an observer-based periodically intermittent controller is initially proposed. Then, stability of the corresponding periodically intermittent control system is analyzed by resorting to piecewise Lyapunov function method. Here, the so-called piecewise Lyapunov function means that Lyapunov function on control time intervals differs from the one on free time intervals. Besides, the existence of an observer-based periodically intermittent controller is converted into the feasibility of linear matrix inequalities. It is worth pointing out that, in comparison with an observer-based continuous controller, the designed observer-based periodically intermittent controller can still retain satisfactory performance with shorter control task execution time. Finally, an illustrative simulation example is given to show the validity and superiority of the result.