This study discusses a new method for approximating compression operators, which play important roles in the operator-theoretic approach to sampled-data systems and time-delay systems. Stimulated by the success in the application of quasi-finite-rank approximation of compression operators defined on the Hilbert space L ₂[0, h), the authors study a parallel problem for compression operators defined on the Banach space L _∞[0, h). In spite of similarity between these problems, they are led to applying a completely different approach because of essential differences in the underlying spaces. More precisely, they apply the idea of the conventional fast-sample/fast-hold (FSFH) approximation technique, and show that the approximation problem can be transformed into such a linear programming problem that asymptotically leads to optimal approximation as the FSFH approximation parameter M tends to infinity. Finally, they demonstrate the effectiveness of the L _∞[0, h)-based approximation technique through numerical examples, with particular application to stability analysis of time-delay systems.

The purpose of this study is to explore the optimal control problems for a class of single spin-1/2 quantum ensembles. The system in question evolves on a manifold in ℛ³ and is modelled as a bilinear control form whose states are represented as coherence vectors. An associated matrix Lie group system with state space SO(3) is introduced in order to facilitate solving the given problem. The controllability as well as the reachable set of the system is first analysed in detail. Then, the maximum principle is applied to the optimal control for system evolving on the Lie group of special orthogonal matrices of dimension 3, with cost that is quadratic in the control input. As an illustrative example, the authors apply their result to perform a reversible logic quantum operation NOT on single spin-1/2 system. Explicit expressions for the optimal control are given which are linked to the initial state of the system.

The regional eigenvalue-clustering robustness problem of grey discrete-time systems with/without state delay is considered. Based on both spectral radius approach and matrix measure approach, three new sufficient conditions are proposed to preserve the regional eigenvalue-clustering property of grey discrete-time systems with/without state delay. If all eigenvalues are only required to be located within the unit circle, the proposed criteria become stability criteria. The proposed sufficient conditions are mathematically proven to be less conservative than those reported in the literature. Three examples are given to demonstrate that the proposed sufficient conditions are applicable and obtain less conservative results compared with those reported recently in the literature.

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.

This study is concerned with the issue of mean-square consensus for a model of leader-following multi-agent system. The agents acting as followers update states based on the information received from the time varying neighbours and the virtual leader. Negative weights besides positive weights are introduced for the links existing among the agents. Moreover, all followers considered here are influenced by noises with different intensities emerging from the external environment or transmission channels. In order to guarantee consensus of the multi-agent system under the noises, the corresponding sufficient conditions are derived. Theoretical proofs are given mainly by using the Lyapunov function approach and the stochastic analysis. Finally, some numerical examples are presented to demonstrate the effectiveness of the results.

This study addresses two issues of robust fault-tolerant stabilisation with circular disk pole constraints for uncertain delta operator switched systems with actuator faults. The first computes the dwell time and proposes a state feedback controller design approach to stabilise the considered switched system. The second solves the 𝒟-stabilisation problem based on state switching strategy. Finally, an illustrative example is provided to validate the feasibility and effectiveness of the proposed approaches.

This study considers the pinning synchronisation in a network of coupled Lur’e dynamical systems under directed topology. By using tools from M-matrix theory, S-procedure and Lyapunov functional method, some simple pinning criteria in terms of linear matrix inequalities, whose dimensions are just determined by the size of a single Lur’e node, are derived for Lur’e networks with fixed and designed inner coupling matrices, respectively. A selective pinning scheme is proposed for a directed Lur’e network such that the network can be globally asymptotically pinned to a homogeneous state. Simulation results are provided to illustrate the effectiveness of the theoretical analysis.

In this study, an electromagnetic levitation system is developed as a prototype for developing active magnetic bearing wheels. The main mechanical parts of the electromagnetic levitation system consists of a rotor, a shaft, a cover and a base. A meaningful electromagnetic force, which is the minimal norm solution to an equation associated with the force and torques of the electromagnetic levitation system, is derived by using the singular value decomposition. A control system using the proportional-integral-derivative controller is developed to levitate the rotor at a target position against the force of gravity and regulate the two gimbal angles of the rotor. The numerical simulation and experimental results on the control of the electromagnetic levitation system are given to demonstrate the validity of the control design presented in this study.