E-grāmata: Nonlinear Systems Stability Analysis: Lyapunov-Based Approach

"The dynamic properties of a physical system can be described in terms of ordinary differential, partial differential, difference equations or any combinations of these subjects. In addition, the systems could be time varying, time invariant and/or time delayed, continues or discrete systems. These equations are often nonlinear in one way or the other, and it is rarely possible to find their solutions. Numerical solutions for such nonlinear dynamic systems with the analog or digital computer are impractical. This is due to the fact that a complete solution must be carried out for every possible initial condition in the solution space. Graphical techniques which can be employed for finding the solutions of the special cases of first and second order ordinary systems, are not useful tools for other type of systems as well as higher order ordinary systems"--

The equations used to describe dynamic properties of physical systems are often nonlinear, and it is rarely possible to find their solutions. Although numerical solutions are impractical and graphical techniques are not useful for many types of systems, there are different theorems and methods that are useful regarding qualitative properties of nonlinear systems and their solutions—system stability being the most crucial property. Without stability, a system will not have value.

Nonlinear Systems Stability Analysis: Lyapunov-Based Approach introduces advanced tools for stability analysis of nonlinear systems. It presents the most recent progress in stability analysis and provides a complete review of the dynamic systems stability analysis methods using Lyapunov approaches. The author discusses standard stability techniques, highlighting their shortcomings, and also describes recent developments in stability analysis that can improve applicability of the standard methods. The text covers mostly new topics such as stability of homogonous nonlinear systems and higher order Lyapunov functions derivatives for stability analysis. It also addresses special classes of nonlinear systems including time-delayed and fuzzy systems.

Presenting new methods, this book provides a nearly complete set of methods for constructing Lyapunov functions in both autonomous and nonautonomous systems, touching on new topics that open up novel research possibilities. Gathering a body of research into one volume, this text offers information to help engineers design stable systems using practice-oriented methods and can be used for graduate courses in a range of engineering disciplines.