Robust Asymptotical Stability and Stabilization of Fractional-Order Complex-Valued Neural Networks with Delay

The robust asymptotical stability and stabilization for a class of fractional-order complex-valued neural networks (FCNNs) with parametric uncertainties and time delay are considered in this paper. It is worth noting that our system combines complex numbers, uncertain parameters, time delay, and fractional orders, which is universal in practical application. Using the theorem of homeomorphism, the sufficient condition of the existence and uniqueness of the equilibrium point for the system is obtained. Then, the sufficient criteria of robust asymptotical stability and stabilization for the addressed models are established, respectively. Finally, we give two numerical examples to verify the feasibility and effectiveness of the theoretical results.

A Mechanical Feedback Classification of Linear Mechanical Control Systems

We give a classification of linear nondissipative mechanical control system under mechanical change of coordinates and feedback. First, we consider a controllable case that is somehow a mechanical counterpart of Brunovský classification, then we extend the result to all linear nondissipative mechanical systems (not necessarily controllable) which leads to a mechanical canonical decomposition. The classification of Lagrangian systems is given afterwards. Next, we show an application of the classification results to the stability and stabilization problem and illustrate them with several examples. All presented results in this paper are expressed in terms of objects on the configuration space Rn only, while the state-space of a mechanical control system is Rn×Rn consisting of configurations and velocities.