Class Of Continuous-time Nonlinear Systems Research Articles

Synchronization in the Lorenz system: Stability and robustness

We present necessary and sufficient conditions for the existence of synchronization in a class of continuous-time nonlinear systems: the so-called ω-affine systems. We apply the results to the Lorenz attractor. The robustness of the synchronization against parameter value variations is discussed using the Lyapunov stability theory for perturbed systems. We obtain sufficient conditions that guarantee a bounded steady-state error. This technique gives conservative results; however, in some systems like that of Lorenz, it provides definitive results about the existence of the synchronization. Furthermore, we give estimates of the maximal error as a function of the difference between the parameter values of the systems to be synchronized.

Identification of a class of nonlinear continuous-time systems using Hartley modulating functions

Most of the existing approaches to identification of nonlinear dynamic systems involve matching a given input-output behaviour with empirical discrete-time approximations such as artificial neural networks, Kolmogorov-Gabor polynomials, radial basis function networks, etc. Techniques for dealing with physically-based continuous-time models are either applicable to only a restricted class of systems or are computationally very demanding. In this paper a new methodology is presented that is applicable to a large class of nonlinear continuous-time systems, by defining a set of Hartley modulating functions for characterizing the continuous process signals. The advantages of this new class of modulating functions are that a set of algebraic equations with real coefficients results, the formulations are free from boundary conditions, and the computations can be made using fast algorithms for the discrete Hartley transformation. The resulting estimation scheme is applied to different categories of nonlinear systems and is tested under both noise-free and noisy conditions.