Impulsive Control Theory

The concept of impulsive control and its mathematical foundation called - pulsive di?erential equations, or di?erential equations with impulse e?ects, or di?erential equations with discontinuous righthand sides have a long history. In fact, in mechanical systems impulsive phenomena had been studied for a long time under di?erent names such as: mechanical systems with impacts. The study of impulsive control systems (control systems with impulse e?ects) has also a long history that can be traced back to the beginning of modern control theory. Many impulsive control methods were successfully developed under the framework of optimal control and were occasionally called impulse control. The so called impulse control is not exactly the impulsive control as will be de?ned in this book. The reader should not mixup these two kinds of control methods though in many papers they were treated as the same. - cently, there is a tendency of integrating impulsive control into hybrid control systems. However, this e?ort does not have much help to the development of impulsive control theory because impulsive systems can only be studied by the very mathematical tool based on impulsive di?erential equations. The e?ort to invent a very general framework of hybrid control system for stu- ing impulsive control and other hybrid control problems will contribute no essential knowledge to impulsive control

This book presents a unified theoretical framework of some recent developments on the impulsive control theory and its applications to engineering problems. Different structures of impulsive control systems and impulsive control strategies are presented. The following theoretical aspects are also addressed: basic knowledge of impulsive differential equations; controllability and stability of linear impulsive control systems; stability of nonlinear impulsive control systems including: practical stability, global stability, absolute stability, stability in terms of two measures; and optimal impulsive control. This book presents also some engineering applications of impulsive control theory. The readers of this book are scientists, engineers, researchers and graduate students interested in impulsive control, nonlinear control systems, chaotic communications systems and nano-electronics.

Preliminaries....Pages 1-15 Linear Impulsive Control....Pages 17-33 Comparison Methods....Pages 35-70 Impulsive Control with Fixed-time Impulses....Pages 71-118 Impulsive Control with Impulses at Variable Time....Pages 119-147 Practical Stability of Impulsive Control....Pages 149-197 Other Impulsive Control Strategies....Pages 199-217 Impulsive Computational Verb Control....Pages 219-235 Impulsive Control of Periodic Motions....Pages 237-287 Impulsive Control of Almost Periodic Motions....Pages 289-306 Applications to Nanoelectronics....Pages 307-333