## Estimation and Design

This chapter analyzes feedback systems and introduces some applications of feedback systems to construct observers. In many practical systems, the entire state vector may not be available. In physical systems, some components of the state are inaccessible internal variables, which either cannot be measured or the measurements require the use of very costly measurement devices. A common way to estimate the state of a system is to build a model of the original system, and then measure the state of this model. In many applications, the original system may change due to some effects such as warming up, wearing out, fatigue, and so on. In such cases the observer will no longer be an exact copy, which can be source of many problems: instability, low speed, poor performance, and so on. The usual way to overcome this difficulty is to design an adaptive observer, which follows the changes of the original system.