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**Linear controller design. Limits of performance.**
*(English)*
Zbl 0748.93003

This book is written on the basis of a novel paradigm. The authors assert that the system of the present controller design should be replaced by that with more sophisticated control algorithms, according to the recent technological development such as high quality integrated sensors and actuators, powerful control processors and computer power both in hardware and software.

The purpose of this book is described in Chapter 1, while discussion and conclusions are stated in Chapter 16, the last chapter. Chapters 2-15 are divided into four parts. The structure of this book is quite vertical and has essentially one story. The essentials of the story are described in Chapters 2, 3, 8-10, and 15. The other chapters, though very important, deal with materials which have ever been published elsewhere. The outlines of each chapter are as follows:

Chapter 2: A new notion of the plant is clearly described. The new notion is quite different from what is used in classical control texts. A particular plant and several controllers for the plant are introduced. These are used in examples throughput this book. Chapter 3: It is stated that the goals of controller design are described in terms of families of Boolean design specifications. Multicriterion optimization and a Pareto optimal specification are described.

Chapter 4: Various norms of both scalar and vector signals are explained. Chapter 5: Various norms of both SISO and MIMO systems are described. Chapter 6: Closed-loop convex design specifications are introduced. Chapter 7: Realizability and internal stability are described. Parametrization of closed-loop transfer matrices achieved by stabilizing controllers is explained. Chapter 8: Input/output specifications and regulation specifications are described. Chapter 9: Differential sensitive specifications with respect to changes in the plant are described. Chapter 10: Robust specifications are explained. A small gain method for robust stability is included. Chapter 11: It is shown that various specifications are indeed convex, using standard examples. Chapter 12: Analytical solutions for the controller are shown. Chapter 13: Some basic tools for convex nondifferential analysis are introduced. Chapter 14: Two convex optimization algorithms are explained: Cutting plane method and ellipsoid algorithm. Chapter 15: Methods for forming and solving finite-dimensional approximation to the controller design problem are described.

The purpose of this book is described in Chapter 1, while discussion and conclusions are stated in Chapter 16, the last chapter. Chapters 2-15 are divided into four parts. The structure of this book is quite vertical and has essentially one story. The essentials of the story are described in Chapters 2, 3, 8-10, and 15. The other chapters, though very important, deal with materials which have ever been published elsewhere. The outlines of each chapter are as follows:

Chapter 2: A new notion of the plant is clearly described. The new notion is quite different from what is used in classical control texts. A particular plant and several controllers for the plant are introduced. These are used in examples throughput this book. Chapter 3: It is stated that the goals of controller design are described in terms of families of Boolean design specifications. Multicriterion optimization and a Pareto optimal specification are described.

Chapter 4: Various norms of both scalar and vector signals are explained. Chapter 5: Various norms of both SISO and MIMO systems are described. Chapter 6: Closed-loop convex design specifications are introduced. Chapter 7: Realizability and internal stability are described. Parametrization of closed-loop transfer matrices achieved by stabilizing controllers is explained. Chapter 8: Input/output specifications and regulation specifications are described. Chapter 9: Differential sensitive specifications with respect to changes in the plant are described. Chapter 10: Robust specifications are explained. A small gain method for robust stability is included. Chapter 11: It is shown that various specifications are indeed convex, using standard examples. Chapter 12: Analytical solutions for the controller are shown. Chapter 13: Some basic tools for convex nondifferential analysis are introduced. Chapter 14: Two convex optimization algorithms are explained: Cutting plane method and ellipsoid algorithm. Chapter 15: Methods for forming and solving finite-dimensional approximation to the controller design problem are described.

Reviewer: K.Ichikawa (Tokyo)

### MSC:

93-02 | Research exposition (monographs, survey articles) pertaining to systems and control theory |

93C05 | Linear systems in control theory |

93B50 | Synthesis problems |