Stability analysis of fractional Quaternion-Valued Leaky Integrator Echo State Neural Networks with multiple time-varying delays

Robust H∞ control of uncertain time-delay Markovian jump quaternion-valued neural networks subject to partially known transition probabilities: direct quaternion method

This paper addresses the issue of robust stochastic stabilization and H ∞ control of uncertain time-delay Markovian jump quaternion-valued neural networks (MJQVNNs) subject to partially known transition probabilities. First, the direct quaternion method is proposed to analyse the MJQVNNs, which is different from some conventional methods in that the former is without any decomposition for systems. After that, in order to estimate the upper bound of the derivative of the constructed Lyapunov-Krasovskii functional (LKF) more accurately, the real-valued convex inequality is extended to quaternion domain. Then, by designed the mode-dependent state feedback controllers, the robust stochastic stabilization conditions of MJQVNNs are given for the admissible uncertainties, and reduce the influence of input disturbance on the controlled output to a specified performance level. Lastly, two numerical examples are given to illustrate the effectiveness of the proposed method.

Guaranteed cost-based feedback control design for fractional-order neutral systems with input-delayed and nonlinear perturbations

Time delay in actuators is mainly caused by electrical and mechanical components. The effect is visible in the system response particularly when changing in the input command. Therefore, input delay is a problem in the control system design that must be taken into account. Besides, ignoring uncertainty in the dynamic models may compromise the controller design. Thus, how to mitigate the effect of this issue on the system stability and performance is a challenging topic. This article deals with the stabilization of fractional neutral systems considering input-delayed and nonlinear perturbations using the guaranteed cost-based feedback control technique. The main focus is to design the state- and output-feedback controllers to achieve a good performance. The stability criteria are formulated in the Lyapunov sense, which are described in terms of matrix inequalities. The proposed idea is validated using simulations.

Robust stability of uncertain fractional order systems of neutral type with distributed delays and control input saturation

Time delay occurs naturally due to the limited bandwidth of any real-world system. However, this problem can deteriorate the system performance and can even result in system instability. Input saturation is also an essential issue due to the energy constraint in real actuators that makes the control design procedure more difficult. This article concerns with the stability of uncertain fractional order (FO) delay systems of neutral type including structured uncertainties, distributed delays and actuator saturation. A Lyapunov-Krasovskii functional allows the formulation of the conditions to insure the asymptotic robust stability of such systems via the linear matrix inequalities (LMI) and to compute the gain of a state feedback controller. In addition, by using the cone complementarity linearization method, we obtain the controller gains that extend the domain of attraction. Several simulations validate the theoretical analysis.