**5. Conclusions**

**Figure 2.** Responses of the second closed-loop NCS.

70 Robust Control - Theoretical Models and Case Studies

**Figure 3.** Responses of the third closed-loop NCS.

In this chapter, we develop an event-triggered static output feedback simultaneous *H<sup>∞</sup>* transmission policy for NCSs under time-varying transmission delay. With the proposed method, we do not need to switch controllers or event-triggered policies for an NCS with several different operating points. Moreover, the reliability of NCSs can be improved as possible element failures can be accommodated. The implementation of the obtained eventtriggered simultaneous *H<sup>∞</sup>* controller is easy as it is in the static output feedback framework. One weakness of our result is that the conditions for the existence of static output feedback simultaneous *H∞* controllers are represented in terms of LMIs with a LME constraint. Standard LMI tools cannot be directly applied to find the solutions. Possible issues for further study include finding less conservative event-triggered transmission policies, considering the possibility of packet dropouts, and relaxing the continuous monitoring requirement at the sensor node by replacing the event-triggered scheme with a self-triggered one.

### **Acknowledgements**

This work was supported by the National Science Council of the Republic of China under Grant NSC 101-2221-E-019-037.

### **Nomenclatures**


*M* >0 (resp., *M* ≥0) the matrix *M* is positive definite (resp., positive semidefinite).

*<sup>M</sup>* <sup>=</sup> *A B* \* *<sup>C</sup>* the symbol \* denotes the symmetric terms in a symmetric matrix

*I* the identity matrix of appropriate dimension.

diag{⋯} the block diagonal matrix.

min *z*( ⋅ ) the minimum value of *z*( ⋅ ).
