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This study introduces a general event triggered framework of state estimation for discrete-time systems with parameter uncertainties residing in a polytope. A robust filter is designed to ensure the ℓ2 stability from disturbance to the estimation error and to minimise the ℓ2 gain subject to both packet rate and size constraints. The number of data transmission and the data size are reduced by the utilisation of an event detector and a logarithmic quantiser, respectively. The event detector compares the current output measurement with the last transmitted measurement: if the difference is beyond a prescribed percentage of the current measurement, then the current measurement is transmitted to the quantiser. The quantiser encodes the measurement before sending to the filter via a digital communication channel. Conditions for filter design are found using polynomially parameter-dependent Lyapunov functions, which generalise the results using quadratic and linearly parameter-dependent Lyapunov functions. The usefulness of the techniques is demonstrated with an illustrative example.

Two systematic methods are presented to guide the construction of Lyapunov functions for general infectious disease models and are thus applicable to establish their global dynamics. Specifically, a matrix-theoretic method using the Perron eigenvector is applied to prove the global stability of the disease-free equilibrium, while a graph-theoretic method based on Kirchhoff's matrix tree theorem and two new combinatorial identities are used to prove the global stability of the endemic equilibrium. Several disease models in the literature and two new cholera models are used to demonstrate the applications of these methods.

We consider interconnections of n nonlinear subsystems in the input-to-state stability (ISS) framework. For each subsystem an ISS Lyapunov function is given that treats the other subsystems as independent inputs. A gain matrix is used to encode the mutual dependencies of the systems in the network. Under a small gain assumption on the monotone operator induced by the gain matrix, a locally Lipschitz continuous ISS Lyapunov function is obtained constructively for the entire network by appropriately scaling the individual Lyapunov functions for the subsystems. The results are obtained in a general formulation of ISS; the cases of summation, maximization, and separation with respect to external gains are obtained as corollaries. [PUBLICATION ABSTRACT]

In this paper, we study the lag synchronization (LS) of n-dimensional hyperchaotic complex nonlinear systems. The idea of the nonlinear control technique based on the complex Lyapunov function with lag in time is used to propose a scheme to investigate LS of hyperchaotic attractors of these systems. Both complex Lyapunov and control functions are introduced. For illustration, the scheme is applied to two hyperchaotic complex Lorenz systems. The real and complex control functions are derived analytically to achieve LS and to show that the complex error dynamical systems are globally stable. Numerical results are calculated to test the validity of the analytical expressions of control functions to achieve LS of two identical hyperchaotic attractors.

This study is concerned with the problem of exponential stability for a class of switched positive linear systems consisting of both stable and unstable subsystems. The sufficient conditions of exponential stability are established in continuous-time and discrete-time domains. Based on the average dwell-time approach, new stability results for such kind of systems are first derived, which allows the ascent of the multiple linear copositive Lyapunov functions caused by unstable subsystems. Furthermore, when all subsystems are stable, the exponential stability condition for switched positive systems is presented. Finally, numerical examples are given to illustrate the effectiveness of the results.

The stability of the zero solution of a nonlinear nonautonomous Caputo fractional differential equation is studied using Lyapunov-like functions. The novelty of this paper is based on the new definition of the derivative of a Lyapunov-like function along the given fractional equation. Comparison results using this definition for scalar fractional differential equations are presented. Several sufficient conditions for stability, uniform stability and asymptotic uniform stability, based on the new definition of the derivative of Lyapunov functions and the new comparison result, are established.

This study studies the problem of synchronisation control for spacecraft formation via extended state observer approach over directed communication topology. The attitude kinematics and dynamics of spacecraft are described by Lagrangian formulations, and the decentralised controller is designed with time-varying external disturbances and unmeasurable velocity information. In particular, the estimation of disturbances obtained via extended state observer is used for the decentralised controller design. A novel Lyapunov function is proposed to show that both static regulation and dynamic synchronisation are realised. Finally, simulation results are given to demonstrate the effectiveness of the controllers proposed in this study.

This manuscript presents a novel 4D chaotic system incorporating transcendental nonlinearities to enhance its complexity and chaotic behavior. The system’s dynamics are analyzed through equilibrium points, bifurcation diagrams, Lyapunov exponents (LEs), sensitivity analysis, basins of attraction, coexistence phenomena, and strange attractors. Impulsive control strategies are employed to establish both local and global stability, validated via Lyapunov-based analysis and numerical simulations. Additionally, synchronization between chaotic systems is explored, demonstrating a robust framework for chaos-based secure communication. The application of the proposed system in secure communications is also discussed.

The direct Lyapunov method is extended to nonlinear Caputo fractional differential equations with variable bounded delays. A brief overview of the literature on derivatives of Lyapunov functions is given and applications to fractional equations are discussed. Advantages and disadvantages are illustrated with examples. Sufficient conditions using three derivatives of Lyapunov functions are given and our results are compared with results in the literature. Also fractional order extensions of comparison principle are established.

Stability of the trivial equilibrium position for a class of hybrid mechanical systems with nonswitched linear velocity forces and switched nonlinear nonhomogeneous positional forces is studied. Sufficient conditions in terms of linear matrix inequalities are obtained to guarantee the existence of a common Lyapunov function for the family of subsystems corresponding to a switched system, and therefore to ensure that the equilibrium position of the switched system is asymptotically stable for an arbitrary switching signal. In the case when we are failed to prove the existence of a common Lyapunov function, classes of switching signals are determined for which one can guarantee the asymptotic stability. An example is presented to demonstrate the effectiveness of the proposed approaches.