Average Dwell Time Property Research Articles

Adaptive Fuzzy Output-Feedback Predefined-Time Control of Nonlinear Switched Systems With Admissible Edge-Dependent Average Dwell Time

This article investigates the adaptive fuzzy output-feedback predefined-time control of nonlinear switched systems with an admissible edge-dependent average dwell time. Different from most of the existing results on neural or fuzzy adaptive finite/fixed-time tracking control of switched systems, where the tracking error goes to a small neighborhood of the origin within finite time, the proposed one can ensure the output tracking error to reach user-defined accuracy within predefined time, which can be arbitrarily preassigned by the designers. Technically, based on the mode-dependent fuzzy state observer, an adaptive output-feedback predefined-time controller is constructed by incorporating a new state-scale transformation function into the barrier Lyapunov function, ensuring predefined transient behavior and tracking accuracy. Besides, by extending the adaptive control problem to the admissible edge-dependent average dwell time framework, the proposed adaptive control scheme can guarantee that all the closed-loop signals are bounded under switching signals with an admissible edge-dependent average dwell time property. It is less conservative than the average dwell time and mode-dependent average dwell time. Finally, two illustrative examples validate the performance of the method presented.

Adaptive Neural Tracking Control Scheme of Switched Stochastic Nonlinear Pure-Feedback Nonlower Triangular Systems

In this paper, we address the adaptive neural tracking control problem for a class of uncertain switched stochastic nonlinear pure-feedback systems with nonlower triangular form. The significant design difficulty is the completely unknown nonlinear functions with all state variables that can neither be directly estimated by radial basis function (RBF) neural networks (NNs) nor be eliminated by the traditional backstepping technique. To achieve the control objective of this paper, a common state-feedback controller for all subsystems is first systematically constructed by using the common coordinate transformation, the variable separation technique, and the universal approximation capability of RBF NNs. Then the stability analysis shows that the semi-global bounded in probability of the whole closed-loop switched system can be obtained and the desired tracking performance can also be insured under a class of switching signals with the average dwell time property. Finally, simulation results are given to demonstrate the effectiveness of the obtained control scheme.

Synchronization for switched neural networks via variable sampled-data control method

Abstract This paper investigates the sampled-data synchronization of switched neural networks with time-varying discrete and distributed delays. Considering that the system switching may happen during a sampling interval, the asynchronous phenomenon is taken into account for the sampled-data control process. By utilizing multiple Lyapunov functions and average dwell time property, sufficient conditions are derived to guarantee the exponential stability of the error between the master and slave neural networks. Based on this, sampled-data controller is further designed so that the master and the slave systems are synchronized with a prescribed performance index. Finally, a numerical example is provided to illustrate the validness and effectiveness of the proposed results.

Stabilisation of continuous‐time switched 2D systems with all unstable modes

This study investigates the stabilisation of a class of continuous-time two-dimensional (2D) switched non-linear Roesser model with all modes unstable. Other than design controllers for the system, the authors would like to schedule the switching signal to achieve the asymptotical stability of the system. The main idea in this study is to utilise the alternative running of different subsystems to compensate the divergence of each subsystem, which thus achieves the stabilisation goal. By taking advantage of mode-dependent average dwell time property and a piecewise continuous Lyapunov function method, a general criterion is developed to guarantee the stability of the continuous-time switched 2D non-linear system with a designed switching law. The obtained result is further used to deal with switched 2D linear system. Finally, the effectiveness and superiority of the proposed methods are illustrated by two numerical examples.

Stability in Switched Cohen‐Grossberg Neural Networks with Mixed Time Delays and Non‐Lipschitz Activation Functions

The stability for the switched Cohen‐Grossberg neural networks with mixed time delays and α‐inverse Hölder activation functions is investigated under the switching rule with the average dwell time property. By applying multiple Lyapunov‐Krasovskii functional approach and linear matrix inequality (LMI) technique, a delay‐dependent sufficient criterion is achieved to ensure such switched neural networks to be globally exponentially stable in terms of LMIs, and the exponential decay estimation is explicitly developed for the states too. Two illustrative examples are given to demonstrate the validity of the theoretical results.

Exponential stability for switched Cohen–Grossberg neural networks with average dwell time

In this paper, uncertain switched Cohen–Grossberg neural networks with interval time-varying delay and distributed time-varying delay are proposed. Novel multiple Lyapunov functions are employed to investigate the stability of the switched neural networks under the switching rule with the average dwell time property. Sufficient conditions are obtained in terms of linear matrix inequalities (LMIs) which guarantee the exponential stability for the switched Cohen–Grossberg neural networks. Numerical examples are provided to illustrate the effectiveness of the proposed method.

Sliding-mode control of switched delay systems with nonlinear perturbations: average dwell time approach

This paper investigates the robust sliding-mode control (SMC) problem for a class of uncertain switched systems with a time delay. The design process of sliding-mode control is divided into two steps. First, a sliding surface is constructed such that the reduced-order equivalent sliding mode restricted to the sliding surface is completely invariant to all admissible uncertainties under switching laws with an average dwell-time property. Second, variable structure controllers are developed to drive the states of the switched delay system to reach the sliding surface in finite time and remain on it thereafter. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.