This book presents multi-stage feedback control designs for the system with multi-time-scale behaviour both in the continuous time domain and discrete-time domain. Multi-time-scale systems have widely separated clusters of eigenvalues, making the system matrices ill-conditioned. Due to this the direct design of a feedback controller and reduced- or full-order observers for such systems is a challenging task. Hence, the feedback controllers and observers are designed in multiple design stages, i.e. two-stage design for the two-time-scale system and three-stage design for the three-time-scale system. In this book, multi-stage feedback controller and observer designs are proposed for the three-time-scale system to reduce offline and online computational efforts. The applicability of these methods is demonstrated by simulating practical systems like a coal-fired power plant and a nuclear power plant.

This book also discusses the design of multi-stage feedback controllers in discrete time. The design of state feedback control for a multi-time-scale system with a lower sampling rate fails to capture information in the fastest (very fast) and fast states. While sampling at a higher rate increases computation time. Thus, the use of single-rate sampling for such systems is unsuitable. Therefore, multi-rate state feedback controllers are designed for the multi-time-scale system, in which slow, fast, and very fast states are sampled at different sampling rates. As slow, fast and very fast states are the decoupled and internal states of the original system, these are estimated by the sequential multi-stage observers. Applications of these multirate designs to the numerical examples are demonstrated and simulations are compared with single-rate sampling methods. The methods suggested in this book result in considerable savings in online and offline computations, reduction in design complexity, and improvement in robustness and closed-loop performance. This book can be beneficial to mathematicians, scientists, researchers and practicing engineers working in this area.