In this study, the authors consider the problem of frequency regulation via output feedback for a hydraulic turbine system under unknown load variations. First, to address the difficulties in estimating the unmeasurable states and the unknown load variation, they introduce a universal finite-time observer (UFTO) which can estimate unmeasurable states, unknown parameters and disturbances under a unified framework. Based on the proposed UFTO, the unmeasurable wicket gate position, the flow rate and the load variation are estimated in a finite time for the hydraulic turbine system. Then by introducing a coordinate transformation, the state-space model of hydraulic turbine system is converted into a simple form for which a state feedback control law is constructed using the adding a power integrator approach. Combining the UFTO with the finite-time control law, an output feedback controller is designed to regulate the frequency of the hydraulic turbine system. Computer simulations are also given to validate the proposed finite-time output feedback controller.

This study investigates the adaptive finite-time consensus protocols for a class of second-order multi-agent systems with unknown non-linear dynamics. Mainly due to the presence of more general unknown non-linearities, the finite-time consensus of multi-agent systems is rather difficult to reach. Radial basis function neural networks are used to approximate the unknown functions. Under some appropriate assumptions, distributed consensus protocols and adaptive laws are designed for all agents. It is proved that the position errors and the velocity errors between any two agents converge to a small neighbourhood of the origin in finite time. Finally, an example of finite-time consensus control for multiple robot systems is given to demonstrate the effectiveness of the proposed method.

Stability of switched linear systems under arbitrary switching signals is an important requirement, when the switching mechanism is unknown, or too complicated to be useful in the stability analysis. In this study, robust exponential stability and exponential stabilisation of parametric uncertain switched linear systems are investigated under arbitrary switching. First, sufficient conditions are proposed to ensure the existence of a common quadratic Lyapunov function (CQLF) for arbitrary switched linear systems with uncertain parameters belong to known intervals. Then, an estimation of stability intervals for uncertain parameters is provided via a theorem. To enlarge the estimated stability intervals, an offline optimisation algorithm is also proposed. Finally, the derived results for robust exponential stability are used to stabilise the uncertain switched linear systems which are not stable under arbitrary switching signals. For this purpose, a method is proposed to design a single state feedback gain in the way that the closed-loop switched linear system is robustly exponentially stable under arbitrarily fast switching signals. Numerical examples are included to demonstrate the effectiveness of the results.

This study proposes a new summation inequality, called the free-matrix-based summation inequality, which further extends certain existing summation inequalities in the literature. Less conservative stability criteria are proposed for discrete-time systems with time-varying delays. Numerical examples are provided to demonstrate the improvement of the proposed approach.

In this study, decentralised region tracking control is proposed to force a group of mobile agents with high-order non-linear dynamics to track a moving target region without collisions as well as to avoid the obstacle on the track in restricted space. The decentralised controllers can also guarantee connectivity preserving of the dynamic interaction network. The control design is based on artificial potential functions, neural network (NN) approximation, adaptive backstepping techniques and Lyapunov's method. It is proved that under the adaptive NN control, the tracking error of each agent can converge to an adjustable neighbourhood of the origin, although some of them do not access the desired region directly. Simulation results are represented to illustrate the performance of the proposed approach.

The synthesis of optimal controllers for vibrational protection of large-scale structures with multiple actuation devices and partial state information is a challenging problem. In this study, the authors present a design strategy that allows computing this kind of controllers by using standard linear matrix inequality optimisation tools. To illustrate the main elements of the new approach, a five-story structure equipped with two interstory actuation devices and subjected to a seismic disturbance is considered. For this control setup, three different controllers are designed: an ideal state-feedback H _∞ controller with full access to the complete state information and two static output-feedback H _∞ controllers with restricted neighbouring state information. To assess the performance of the proposed controllers, the corresponding frequency responses are investigated and a proper set of numerical simulations are conducted, using the full scale North-South El Centro 1940 seismic record as ground acceleration input. The obtained results indicate that, despite the severe information constraints, the proposed static output-feedback controllers attain a level of seismic protection that is very similar to that achieved by the ideal state-feedback controller with complete state information.

This study is concerned with the observer-based H _∞ stabilisation problem for a class of linear systems with large delay periods (LDPs). Based on the switching technique, the system with LDPs is modelled into a switched delay system which consists of two subsystems. The controller and observer gains are solved under the small delay case. Sufficient conditions are derived to ensure the system is not only exponentially stable, but also possesses an H _∞ performance index. The effectiveness of the proposed method is validated by the simulation of a load frequency control system.

This study focuses on the design of a switching controller, which includes several linear time-invariant (LTI) controllers designed beforehand and independently, for a specific LTI plant. All of these LTI controllers are capable of stabilising the plant with corresponding H _∞ control performance criterions. It is shown that there exist suitable state space realisations of these controller transfer matrices that guarantee not only certain H _∞ control performance of the overall closed-loop system under arbitrary switching but also corresponding H _∞ performances of local closed-loop systems at switching points.

This study proposes a fast and stable recursive ellipsoidal state-bounding-based set-membership estimation algorithm for the state estimation of linear system with unknown-but-bounded (UBB) disturbances. The proposed algorithm has a prediction–correction structure in time update and observation update, which is similar to Kalman filter. For both time update and observation update, there is a data-depending weighting factor. The observation weighting factor is acquired by minimising the upper bound on a Lyapunov function of the posteriori estimation error. It has been demonstrated that the estimation error of the proposed algorithm is input-to-state stable when the system is uniformly observable. With the property of selective observation update, the proposed algorithm not only improves the point estimation accuracy but also decreases the computation load of observation weighting factors and the volume of feasible ellipsoid sets. The efficiency of the proposed algorithm has been demonstrated by numerical simulations with different UBB disturbances.

This study addresses the leader–follower consensus problem for multi-agent systems with directed graphs where each agent is modelled as a non-linear Lur'e system. Both the cases where the leader has zero or bounded control inputs are considered. For the case where the leader is of zero control input, a distributed adaptive protocol is designed, under which leader–follower consensus can be achieved for any directed graph containing a directed spanning tree with the leader as the root. For the case where the leader's control input is unknown, but bounded, a novel continuous distributed adaptive protocol is proposed to guarantee the uniform ultimate boundedness of the consensus error and the adaptive coupling gains. The upper bound of the consensus error is also explicitly derived. In comparison to the existing literature, the main contribution of this paper is that the adaptive protocols in this study are fully distributed and meanwhile applicable to a wide class of directed graphs.

This study studies the exponential state consensus problem for hierarchical multi-agent dynamical systems with switching topology and inter-layer communication delay. A Lyapunov function is introduced to quantify the total disagreement among the nodes of a hierarchical multi-agent system. By using the stability theory of switched system and graph theory of hierarchical network topology, delay dependent sufficient conditions are proposed to achieve the exponential hierarchical average consensus with the average dwell time of the switching law larger than a minimum bound. Illustrative examples are provided to verify the effectiveness of the proposed approach.

For a discrete-time linear system with uncertain model perturbations and additive disturbances, the authors develop an approach to evaluate the explicit state feedback solution of the constrained min–max model predictive control problem. By considering a quadratic cost function and a robust reformulation of constraints, the problem is transferred to an equivalent multi-parametric programming problem. The control policy is determined to be a continuous and piecewise affine function of the state vector. Meanwhile, the feasible state space is partitioned into polyhedral cones corresponding to the control law. The results are shown via computer simulations by applying the method to a numerical example.

This study considers the problem of anti-windup (AW) controller design for singularly perturbed systems with actuator saturation. The AW controller consists of a dynamic state feedback (DSF) controller and an AW compensator. A convex optimisation problem in terms of linear matrix inequalities is formulated to simultaneously design both the DSF controller and the AW compensator. The resulting AW controller depends on the singular perturbation parameter ɛ and is shown to be well-conditioned for any ɛ of interest. Furthermore, a two-stage design method is proposed to handle the case that ɛ is unknown. An ɛ-independent DSF controller is designed at the first stage, and then an ɛ-independent AW compensator is constructed by solving a convex optimisation problem. Both of the methods can achieve a desired stability bound and enlarge the basin of attraction at the same time. Finally, examples are given to show the advantages and effectiveness of the obtained results.

To characterise complete controllability of a time-varying linearised error system of a given non-linear system, this study focuses the attention on hyper-regularity of a polynomial matrix derived from the non-linear system and introduces the concept called controllable trajectory. It is shown that if a polynomial matrix derived from a given non-linear system is hyper-regular, then every linearised system along any controllable trajectory is completely controllable. Through a non-holonomic mobile robot example, it is demonstrated that if a polynomial matrix derived from a given non-linear system is hyper-regular, and if a reference trajectory is the state part of a periodic controllable trajectory, a trajectory tracking control is achieved by a two-degree-of-freedom controller design method.