Standard output regulation design techniques cannot be applied for linear two-time-scale systems subject to saturated inputs. In this work, a state feedback output regulation is first proposed based on a classical stabilizing composite state feedback controller. Nevertheless, the corresponding design is difficult to implement due to numerical issues. Thus, the method of asymptotic power series expansion is applied to provide an approximate solution to the regulator equation. Then, a time-continuous state feedback controller is designed by combining the Chang transformation approach and the low-gain feedback technique, which results in a semi-global bounded output regulation of the closed-loop system. Furthermore, to reduce control updates, a dynamic event-triggered control scheme is proposed which ensures the exclusion of Zeno behavior by maintaining a strictly positive time between any two triggering moments, regardless of the initial state of the system. Additionally, an observer-based event-triggered control scheme is proposed to cater to the practical scenario in which system state information is unavailable. Finally, to demonstrate the effectiveness of our proposed technique, two examples are presented.

This article proposes the design of an event-triggered control strategy for consensus of interconnected two-time scales systems with structured uncertainty. The control design under consideration ensures also that consensus is achieved with an overall guaranteed cost. Since each system involves processes evolving on both fast and slow time scales, two Zeno-free event-triggered mechanisms are designed to independently decide the sampling and transmission instants for the slow and fast states, respectively. As the first step, we design an event-triggering consensus protocol in the ideal/nominal case when the interconnected systems are not affected by uncertainties and the interactions happen over a fixed interaction network. Next, the results are extended in order to take into account structured uncertainties affecting the systems' dynamics. At this step, we go further and we provide sufficient conditions for event-triggering consensus with a guaranteed overall cost. Finally, two numerical examples are provided to demonstrate the effectiveness of the proposed theoretical results.

In this brief, we investigate the fixed-time synchronization of competitive neural networks with multiple time scales. These neural networks play an important role in visual processing, pattern recognition, neural computing, and so on. Our main contribution is the design of a novel synchronizing controller, which does not depend on the ratio between the fast and slow time scales. This feature makes the controller easy to implement since it is designed through well-posed algebraic conditions (i.e., even when the ratio between the time scales goes to 0, the controller gain is well defined and does not go to infinity). Last but not least, the closed-loop dynamics is characterized by a high convergence speed with a settling time which is upper bounded, and the bound is independent of the initial conditions. A numerical simulation illustrates our results and emphasizes their effectiveness.

This paper proposes and analyzes a stochastic multiagent opinion dynamics model. We are interested in a multi-leveled opinion of each agent which is randomly influenced by the binary actions of its neighbors. It is shown that, as far as the number of agents in the network is finite, the model asymptotically produces consensus. The consensus value corresponds to one of the absorbing states of the associated Markov system. However, when the number of agents is large, we emphasize that partial agreements are reached and these transient states are metastable, i.e., the expected persistence duration is arbitrarily large. These states are characterized using an N-intertwined mean field approximation (NIMFA) for the Markov system. Numerical simulations validate the proposed analysis.