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This paper investigates the aperiodic sampling stabilisation problem for a class of switched linear systems under asynchronous switching. Based on a novel dynamic sampling rule, a sampling-point-based partition-dependent discontinuous Lyapunov functions control approach are developed to make the considered closed-loop switched systems be globally asymptotically stable. Compared with the existing results, the proposed control method permits frequent switching in a sampling interval for subsystems. But the frequent information transmission to the matched controllers and the negative effect of long asynchronous running on system performance can be nicely handled in this paper. Moreover, the partitioned Lyapunov functions are allowed to increase in some segments of the synchronous operating intervals. Tighter synchronous duration and switching number which are determined by more than affine functions make the switching signal more flexible. Finally, simulation analyses of two examples show the advantages of the developed control strategy. [ABSTRACT FROM AUTHOR]

This paper concerns to an event-triggered control for switching linear systems. For reducing the data transmission amount of the communication network from sensor to controller, a switching-mode independent dynamic event-trigger (DET) is constructed wherein a positive constant and a positive auxiliary variable are simultaneously involved. Based on the received discrete-time state measurements, a mode-dependent feedback control law is proposed. Given some prior activation probabilities of switching signal, an average dwell time (ADT) based controller designed method is presented. It is proved that the closed-loop system achieves Zeno-free mean square bounded exponentially stable (MSBES). Significantly, the minimal event-triggered interval can be accurately given while the maximal event-triggered interval can be approximated. Numerical examples are provided to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper presents a systematic method to design a high-order repetitive model reference controller (HO-RMRC) for a discrete-time linear system that is subject to uncertain periodic references and disturbances. The controller design method we propose is established by combining two controller design schemes: high-order repetitive control (HORC) and model reference control (MRC). Here, the HORC is used to suppress uncertain periodic disturbances significantly and the MRC is used to track time-varying references without introducing new transient responses. The stability analysis of the resulting closed-loop system is provided and describes how admissible learning gains are determined to achieve stability and a desirable convergence rate. The efficacy of the proposed control method is demonstrated via numerical simulations where the performance of the resulting HO-RMRC is compared with those of the HORC and the MRC as standalone controllers. It is evident that the HO-RMRC outperforms the HORC and the MRC in simultaneously achieving perfect reference tracking and disturbance cancellation/attenuation. [ABSTRACT FROM AUTHOR]

This paper deals with the stabilisation problem of linear systems subject to saturated input and bounded disturbance via event-triggered control strategy. In a hybrid systems framework, both a state feedback law and a static output feedback law are proposed to design the event-triggered controllers, which provide solutions to the event-triggered control collaborative design problem. For the case of using static output feedback, an iterative linear matrix inequality algorithm is proposed to obtain the feedback gain. In addition, the local uniform ultimate boundedness of the closed-loop system is ensured. Finally, two examples are given to illustrate the effectiveness of the proposed controllers. [ABSTRACT FROM AUTHOR]

In this paper, high-order fully actuated (HOFA) models with multiple orders for general dynamical control systems are firstly proposed, for which controllers can be easily designed such that the closed-loop systems are constant linear ones with completely assignable eigenstructures. Based on this special feature of the type of HOFA models, controllability of general dynamical control systems is proposed. It is revealed that a general dynamical control system can be represented by a controllable subsystem described by a HOFA model, and an extra uncontrollable one or supplementary one. While a general dynamical control system is called stabilisable if its uncontrollable (autonomous) subsystem does not exist, or is stable in a certain sense. Finally, two parametric design approaches for control of the type of general HOFA models are proposed, which provide all the design degrees of freedom. Several examples, including ones of sub-fully actuated systems, are treated, which demonstrate the effect of the proposed theories. [ABSTRACT FROM AUTHOR]

This paper deals with the state feedback control for linear systems in the presence of state delay using a direct numerical design methodology. The design algorithm iteratively searches the solution space of controller parameters to find a proper controller gain that guarantees the delay-independent stability of the closed-loop system. The algorithm divides the solution space to some simplexes, selects one simplex and evaluates two checking methods on this simplex. The first method checks the stabilisability of the corner points (to establish the feasible point) and the other detects the total infeasibility (total de-stabilisability) of the simplex (to omit the undesired parts). One interesting property of the method is its capability in detecting total de-stabilisability of a simplex through its corner points. If none of these methods is successful, the simplex is divided into two smaller ones which will be checked in the next algorithm's iterations. According to the direct search nature, the algorithm is non-conservative and assuredly reaches a stabilizable point in the feasible space of the design space. The proposed algorithm and previous methods are evaluated on a set of random generated systems to compare the feasibility of the methods. Simulation results reveal the superiority of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This paper studies the h-stabilisation problem of certain classes of perturbed systems on time scales. Sufficient conditions for the control law design are proposed to ensure the h-stability of the closed-loop dynamical system under Lipschitz-type disturbances. Using the Gronwall inequality approach with time scale theory, the h-stability of the closed-loop system is investigated in non-uniform time domains with bounded graininess. Some numerical examples are provided to show the feasibility of the obtained results using the proposed approach for systems evolving on some arbitrary time scales. [ABSTRACT FROM AUTHOR]

In this paper, the model-based event-triggered control is addressed for a class of linear systems with two time scales. The singular perturbation technique is used to analyse the stability of the event-triggered control closed-loop system with a dual-stage event-triggering condition. For the differences between the matrices of the plant and the model, the relations between the parameters in the event-triggering conditions are revealed for the stability and the sampling performance of the closed-loop systems. Specifically, the parameters in the event-triggering conditions can be selected in a range independent of the matrices in the model. Finally, two numerical simulations are provided to illustrate the efficiency and feasibility of the proposed results. [ABSTRACT FROM AUTHOR]

In this paper, the preview control problem for a class of linear continuous time stochastic systems with multiplicative noise is studied based on the augmented error system method. First, a deterministic assistant system is introduced, and the original system is translated to the assistant system. Then, the integrator is employed to ensure the output of the closed-loop system tracking the reference signal accurately. Second, the augmented error system, which includes integrator vector, control vector and reference signal, is constructed based on the system after translation. As a result, the tracking problem is transformed into the optimal control problem of the augmented error system, and the optimal control input is obtained by the dynamic programming method. This control input is regarded as the preview controller of the original system. For a linear stochastic system with multiplicative noise, the difficulty being unable to construct an augmented error system by the derivation method is solved in this paper. And, the existence and uniqueness solution of the Riccati equation corresponding to the stochastic augmented error system is discussed. The numerical simulations show that the preview controller designed in this paper is very effective. [ABSTRACT FROM AUTHOR]

A two-steps method of designing switched linear systems is presented with the parameterization of globally uniformly asymptotically stabilising controllers with average dwell time (ADT). First, an observer-based switching controller design is given for a class of switched linear system. Based on the construction of observer-based controller, conceptions of doubly coprime factorization and Youla parameterization of LTI systems are extended to switched linear systems with respect to globally uniformly asymptotical stability (GUAS) using a state-space expression. Second, the parameterization of closed-loop systems, which are affine with any globally uniformly asymptotically stable -parameter, is then described. This description enables the application of the -- parameter approach to a variety of switched linear control-system designs. The control construction provides us a two-steps process design procedure. Above all, based on the Schur complementary lemma and controller variable elimination method, a systematic weighted L2 performance strategy is focused on and a design scheme of to obtain weighted L2-gain performance is clarified. Finally, a numerical example is given to show the validity and potential of the developed results. [ABSTRACT FROM AUTHOR]

The paper is concerned with the control of a linear plant with an output delay. As is known, when the plant parameters do not vary in time, the transfer function approach can be used to find a high-performing controller with the Smith-predictor structure. Such an approach in the domain of the Laplace transform is not directly applicable in the time-variant case. Nevertheless, it is shown that the transfer function of the Smith controller valid for constant values of the parameters can be realised in such a way that closed-loop stability, as well as point-wise optimal performance, is ensured also when the parameters vary with time. The suggested technique is applied to the control of a heat exchanger whose varying parameters include a measurement delay. [ABSTRACT FROM AUTHOR]