Systems with Multiple Nonlinear Feedback Controls

As a result of the fast development of science and technology, control systems have become more and more complex. Usually, single feedback control is not enough to finish a complicated task and needs multiple feedbacks. In 1988, SIAM published a research report “The Future Development of Control Theory – Mathematical Prospect.” It was indicated in this report that though the stability of nonlinear control systems had been paid much attention and many mathematical results had been found, the results are still mainly on single-variable nonlinear control systems such as Popov’s principal and Lyapunov method. Multivariable nonlinear control systems are not yet well generalized. It is still difficult to extend the single-variable case to the multivariable case.

In this chapter, we will discuss the absolute stability of control systems with multiple nonlinear control terms. The results given in Sects. 7.1–7.4 are taken from Liao et al. [91, 92], and that presented in Sect. 7.5 are from Gan and Ge [29].