Singular perturbations and time-scale techniques were introduced to control engineering in the late 1960s and have since become common tools for the modeling,
analysis and design of control systems. The 1986 edition of this book, reprinted here in its original form, provides the theoretical foundation for representative control applications. Its bibliography includes more than 400 references. Their number has been steadily growing since the 1986 publication of the book.
Recent publications show a significant diversification in control applications of singular perturbation techniques. Most current developments can be divided in three groups. The first group comprises the use of singular perturbations in new control problems. One of these stresses the geometric ("slow manifold") aspect of two-time-scale systems and provides, via high-gain feedback, an interpretation of the important concept of zero dynamics. Multi-time-scale behavior is also analyzed in high-gain observers, which are employed for semiglobal stabilization of nonlinear systems. A singular perturbation analysis reveals the dangers of large magnitude transients ("peaking") in high-gain feedback systems and serves as a basis for low-gain/high-gain designs in which such undesirable transients are avoided. Singularly perturbed Hm control systems have also been studied, including H estimators with small noise.