Dealing with impulsive effects is one of the most challenging problems in the field of fixed-time control. In this paper, we solve this challenging problem by considering fixed-time synchronization of complex networks (CNs) with impulsive effects. By designing a new Lyapunov function and constructing comparison systems, a sufficient condition formulated by matrix inequalities is given to ensure that all the dynamical subsystems in the CNs are synchronized with an isolated system in a settling time, which is independent of the initial values of both the CNs and the isolated system. Then, by partitioning impulse interval and using the convex combination technique, sufficient conditions in terms of linear matrix inequalities are provided. Our synchronization criteria unify synchronizing and desynchronizing impulses. Compared with the existing controllers for fixed-time and finite-time techniques, the designed controller is continuous and does not include any sign function, and hence, the chattering phenomenon in most of the existing results is overcome. An optimal algorithm is proposed for the estimation of the settling time. Numerical examples are given to show the effectiveness of our new results.

For switched linear parameter-varying (LPV) systems with possible actuator failures, the parameter-dependent multiple piecewise Lyapunov function is constructed to handle the $H_\infty$ bumpless transfer fault-tolerant control problem. First, a generalized bumpless transfer concept is presented for switched LPV systems to describe the transient performance, for which only the local bumpless transfer condition is required. Second, an event-triggered switching law, depending on the system states, external parameters, and dwell time, is designed to ensure a time span among adjacent switchings. Third, a solvability condition of the $H_\infty$ bumpless transfer fault-tolerant control problem is developed. A family of time-driven switching controllers with bumpless transfer constraint and fault-tolerant requirement are also designed. Finally, an application example of an aero-engine is given to verify the effectiveness of the developed methods.

The problem of event-triggered synchronization of master-slave neural networks is investigated in this article. It is assumed that both communication channels from the sensor to controller and from controller to actuator are subject to stochastic deception attacks modeled by two independent Markov processes. Two discrete event-triggered mechanisms are introduced for both channels to reduce the number of data transmission through the communication channels. To comply with practical point of view, static output feedback is utilized. By employing the Lyapunov-Krasovskii functional method, some sufficient conditions on the synchronization of master-slave neural networks are derived in terms of linear matrix inequalities, which make it easy to design suitable output feedback controllers. Finally, a numerical example is presented to show the effectiveness of the proposed method.

This paper considers the stochastic stability and the robust control of descriptor discrete-time systems with Markovian jumping parameters. In terms of linear matrix inequalities, a necessary and sufficient condition is proposed, which ensures a discrete-time descriptor Markovian jump system to be regular, causal and stochastically stable. A robust admissibility condition and a robust bounded real lemma are also developed. Based on these, a sufficient condition on the existence of a state-feedback controller which guarantees the robust admissibility and the performance is also given by employing the linear matrix inequality technique. A robustly stabilizing state feedback controller can be constructed through the numerical solutions of linear matrix inequalities. Finally, an example is provided to demonstrate the effectiveness of the proposed approach.

This article deals with the robust H ₂ control problem for a class of Markovian jump linear systems with uncertain switching probabilities. The uncertainties under consideration appear both in the system parameters and in the mode transition rates. First, a new criterion based on linear matrix inequalities is established for checking the robust H ₂ performance of the uncertain system. Then, a sufficient condition for the existence of the state-feedback controllers is established such that the closed-loop system is quadratically mean square stable and has a certain level of robust H ₂ performance in terms of linear matrix inequalities with equality constraints. A globally convergent algorithm is also presented to construct such controllers effectively. Finally, an illustrative numerical example is used to demonstrate the developed theory.