In this study, automated generation of linear parameter-varying (LPV) state-space models to embed the dynamical behaviour of non-linear systems is considered, focusing on the trade-off between scheduling complexity and model accuracy and the minimisation of the conservativeness of the resulting embedding. The LPV state-space model is synthesised with affine scheduling dependency, while the scheduling variables themselves are non-linear functions of the state and input variables of the original system. The method allows to generate complete or approximative embedding of the non-linear system model and also it can be used to minimise the complexity of existing LPV embeddings. The capabilities of the method are demonstrated on simulation examples and also in an empirical case study where the first-principle motion model of a three degrees of freedom (3DOF) control moment gyroscope is converted by the proposed method to an LPV model with low scheduling complexity. Using the resulting model, a gain-scheduled controller is designed and applied on the gyroscope, demonstrating the efficiency of the developed approach.

The flocking of a multi-agent system with dynamic topology is investigated in this study. A switching control law is developed to achieve the flocking by adding the controls from some of type II uninformed agents to their closest informed agent including the non-linear relative velocity feedback. The multiple Lyapunov functions are then constructed and a stable analysis for the flocking is given based on the LaSalle invariance principle. It is proven that the energy is bounded at all time, and asymptotically converges to the state of minimum energy; the velocities of all the agents approach the velocity of the virtual leader asymptotically; no collision happens between the mobile agents. The effects of the number of informed agents and non-linear relative velocity feedbacks on the flocking are also investigated. It is shown that fewer informed agents in comparison with existing methods can guarantee stable flocking, which is very significant in some practical applications for secure communication.

In this study, a novel distributed adaptive controller is provided for consensus control of high-order non-linear multi-agent systems with unknown time-varying delays. The system is subject to uncertain disturbances, and the agents' dynamics are not known. Unlike the existing literature, the proposed method does not require time-delay terms in system dynamics to be bounded. A neural network is used to model the unknown non-linear dynamics. Then, despite the destabilising effect of the unknown delays, some adaptive rules based on the dynamic surface control are designed to achieve the consensus objective. The semi-global uniform boundedness of the resultant closed-loop signals and the convergence of the tracking errors to a neighbourhood of the origin are shown mathematically. Simulations verify the effectiveness of the results.

This study deals with the multiple Lyapunov functions approach for the robust leader-following consensus of one-sided Lipschitz (OSL) multiagents, connected via switching topologies under external disturbances. Disturbances have been accounted for followers, connected via a directed graph with a spanning tree from the leader root. The authors stipulate two consensus protocols, based on the absence or existence of norm-bounded reference input to the leader, and provide matrix inequalities for designing the parameters of consensus controllers. In the presence of bounded disturbances, the proposed protocol ensures consensus criterion for minimisation of the effect of disturbances to the consensus error between the leader and followers. A remedy for striking robustness against external perturbations has been provided in the present work in contrast to the conventional consensus schemes on OSL agents. Switching OSL mobile agents and aircraft carriers consisting of a leader and five followers have been simulated in the existence of reference input and disturbances to demonstrate the empirical proficiency of the consensus protocol schemes.

For Markov switched stochastic functional differential systems (SFDSs), asymptotic property is one of the most desired issues. Recently, a new class of delay-dependent asymptotic stability for non-linear Markov switched SFDSs was investigated. However, the existing references do not take the convergent speed and non-autonomous factor into consideration. Therefore, by means of multiple Lyapunov–Krasovskii functionals, this study is devoted to examine the exponential stability for highly non-linear autonomous Markov switched SFDSs and the exponential stability, polynomial stability and polynomial growth at most for highly non-linear non-autonomous systems, where all the criteria rely on the intervals lengths of continuous delays. In addition, the properties of boundedness and asymptotic stability are as well explored.