Numerical Approximation of Lyapunov Exponents and its Applications in Control Systems

The progression of state trajectories with respect to time, and its stability properties can be described by a system of nonlinear differential equations. However, since most nonlinear dynamical systems cannot be solved by hand, one must rely on computer simulations to observe the behavior of the system. This work focuses on chaotic systems. The Lyapunov Exponent (LE) is frequently used in the quantitative studies of a chaotic system. Lyapunov exponents give the average rate of separation of nearby orbits in phase space, which can be used to determine the state of a system, e.g. stable or unstable. The objective of this research is to provide control engineers with a convenient toolbox for studying the stability of a large class of control systems. This toolbox is implemented in MatLab with structured programming so that it can be easily adapted by users