**Graphical Method for Robust Stability Analysis for Time Delay Systems: A Case of Study**

Gerardo Romero, David Lara, Irma Pérez and Esmeralda Lopez

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/63158

### **Abstract**

**References**

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This chapter presents a tool for analysis of robust stability, consisting of a graphical method based on the construction of the value set of the characteristic equation of an interval plant that is obtained when the transfer function of the mathematical model is connected with a feedback controller. The main contribution presented here is the inclusion of the time delay in the mathematical model. The robust stability margin of the closed-loop system is calculated using the zero exclusion principle. This methodology converts the original analytic robust stability problem into a simplified problem consisting on a graphic examination; it is only necessary to observe if the value-set graph on the complex plane does not include the zero. A case of study of an internal combustion engine is treated, considering interval uncertainty and the time delay, which has been neglected in previous publications due to the increase in complexity of the analysis when this late is considered.

**Keywords:** robust stability, robustness margin, polynomials of Kharitonov, value set, interval uncertainty
