Absolute stability of nonlinear control systems


Absolute stability of nonlinear control systems

[by] Liao Xiaoxin

(Mathematics and its applications, . Chinese series)

Kluwer Academic Publishers , Science Press, c1993

  • : Kluwer
  • : Science Press

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Includes index



This volume presents an overview of some recent developments on the absolute stability of nonlinear control systems. Chapter 1 introduces the main tools and the principal results used in this book, such as Lyapunov functions, K-class functions, Dini-derivatives, M-matrices and the principal theorems on global stability. Chapter 2 presents the absolute stability theory of autonomous control systems and the well-known Lurie problem. Chapter 3 gives some simple algebraic necessary and sufficient conditions for the absolute stability of several special control systems. Chapter 4 discusses nonautonomous and discrete control systems. Chapter 5 deals with the absolute stability of control systems with m nonlinear control terms. Chapter 6 devotes itself to the absolute stability of control systems described by functional differential equations. The book concludes with a useful bibliography. It is for applied mathematicians, and engineers whose work involves control systems.


  • Principal theorems on global stability
  • autonomous control systems
  • special control systems
  • non-autonomous and discrete control systems
  • control systems with m non-linear control terms
  • control systems described with FDE.

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