Focusing on input-to-state stability (ISS) for partial differential equations, this book introduces novel tools specifically designed for parabolic and hyperbolic classes. It establishes a comprehensive framework for analyzing these equations, enhancing the understanding of stability in a mathematical context. The work is essential for researchers and practitioners in the field, providing critical insights and methodologies for tackling complex PDEs.
This book offers a clear and comprehensive overview of nonlinear control systems, focusing on stability and feedback stabilization techniques. It covers global stability properties, various nonlinear systems, and introduces new tools for analysis and design. Theoretical insights are complemented by practical applications and examples, making it valuable for researchers and graduate students alike.
This monograph bridges the gap between the concept of nonlinear predictors and their practical application, offering a comprehensive theory for using predictor feedback in time-invariant, uncertain systems with constant input and measurement delays. It presents various methods for generating real-time solutions to the nonlinear differential equations, termed approximate predictors. Part I introduces predictor feedback for linear time-invariant (LTI) systems, establishing foundational concepts due to their simpler nature compared to nonlinear systems. Part II extends these concepts to nonlinear time-invariant systems, while Part III explores applications to systems described by integral delay equations and discrete-time systems. The core focus is on designing control and observer algorithms that maintain global stabilization, previously guaranteed with idealized predictors, using the approximate predictors developed in the book. Engineers will appreciate numerous explicit formulas provided to aid in applying the theory to various control problems. Mathematicians will find sophisticated proof techniques aimed at ensuring global stability for nonlinear infinite-dimensional delay systems under feedback laws utilizing practically implementable approximate predictors. Researchers and graduate students in systems and control will benefit from this monograph as a valuable resource for advancing their understanding of nonlinear control
