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Time-delay systems are widely used in industrial applications, such as chemical process and aerospace. The predictor-based feedback method is one of the effective ways to deal with such systems. This paper studies the delay compensation problem for linear systems with multiple distributed input delays. A novel state vector associated with the future state of the system is constructed, which reduces the original linear time-delay system to a linear delay-free system. Memory feedback controller is then designed, and necessary and sufficient conditions for the stability of the closed-loop system are acquired in accordance with the stability of an integral delay system. To avoid the difficult implementation problem of memory feedback controller, the memoryless feedback controller is proposed instead to compensate the multiple distributed input delays. Finally, the proposed controllers are applied to the design of the linearized liquid-level control resonant circuit system. [ABSTRACT FROM AUTHOR]

A family of observer‐based periodic delayed feedback (PDF) controllers are proposed in this paper for the fixed‐time stabilization of the linear input‐delay system with immeasurable states. By switching the controller gain to different values periodically, an explicit relationship is established between the control gain and the system matrix. To address the open‐loop problem faced by the standard PDF controller, two different observer‐predictor‐based PDF are proposed. Both controllers ensure that the closed‐loop system converges asymptotically throughout the control period. Furthermore, a modified PDF is proposed for multi‐input‐multi‐output systems utilizing the characteristic of controllability index set and observability index set. The modified PDF can be used for the reduction of switches required in the stabilization. A simulation example on the spacecraft rendezvous is proposed to illustrate the theory of the method proposed. [ABSTRACT FROM AUTHOR]

Summary: This paper is concerned with the disturbance rejection control problem of multiple integrators systems subject to actuator saturation and external disturbance. By using the solutions to a class of parametric Lyapunov equations (PLEs), extended observer based bounded linear output feedback controller is designed to solve the considered problem. By constructing a novel Lyapunov function and using the properties of the PLE, the stability of the closed‐loop system is proved and the domain of attraction is estimated. In order to improve control performance, bounded linear time‐varying output feedback controller is also proposed such that the state of the closed‐loop system tends to zero as the time approaches to the prescribed setting time which is independent of the initial conditions and can be assigned in advance. In addition, some comparisons of the proposed methods to existing results are given. Finally, numerical examples verify the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

This paper studies the problem of pole assignment for high-order discrete-time linear systems with multiple state and input delays. When the number of state delays is larger than or equal to that of input delays, an effective predictor feedback controller is proposed based on the augmented technique, and the design process for the feedback gain is also presented. In addition, it is proved that the pole assignment problem is solvable if and only if the solutions to a linear matrix equation are such that a matrix is nonsingular. When the number of state delays is smaller than that of input delays, the original system is first transformed into a delay-free system with keeping the system controllability invariant, and then, the corresponding controller with designable feedback gain is established. To characterize all of the feedback gains, a factorization approach is introduced which can provide full degree of freedom. Numerical examples are employed to illustrate the effectiveness of the proposed approaches. [ABSTRACT FROM AUTHOR]

The consensus problem for multiagent systems (MASs) described by discrete-time linear systems with multiple input delays is investigated. Under two reasonable assumptions, a truncated pseudo-predictor feedback (TPPF) approach is established to solve the consensus problem. The proposed TPPF protocols allow arbitrarily large yet bounded delays and are easy to implement in practice since they are finite dimensional and only use the relative current state information of neighboring agents. Moreover, the proposed protocols can also achieve semi-global consensus of MASs if the actuators are subject to saturations. A numerical example is given to illustrate the effectiveness of the proposed approaches. [ABSTRACT FROM AUTHOR]

Abstract This paper investigates the global stabilization problem of discrete-time multiple integrators with bounded and delayed feedback. In the absence of input delay, two classes of nonlinear feedback laws are proposed. The first one consists of parallel connections of saturation functions and the other one consists of nested saturation functions. Some free parameters and the so-called state-dependent saturation functions are introduced into these two types of control laws which can help to improve the transient performance of the closed-loop system. In the presence of input delay, with the aid of a special canonical form, two types of nonlinear control laws are also proposed to achieve global stability of the closed-loop system. Two numerical examples are given to illustrate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

The problem of global stabilization for the multiple oscillator systems by bounded and delayed controls is considered. Based on a special canonical form of the considered system, a nonlinear control law consisting of nested saturation functions is proposed to achieve global stabilization. The new special canonical form used in this brief contains not only time delay in the input but also time delays in its state, which leads to natural cancellation and helps to not only provide explicit conditions guaranteeing the global stability of the closed-loop systems but also improves the transient performance of the closed-loop system significantly. The proposed feedback law is also adopted to achieve restricted tracking. A numerical simulation is given to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper studies the problems of stabilization of discrete-time linear systems with a single input delay. By developing the methodology of pseudo-predictor feedback, which uses the (artificial) closed-loop system dynamics to predict the future state, memoryless state feedback control laws are constructed to solve the problem. Necessary and sufficient conditions are obtained to guarantee the stability of the closed-loop system in terms of the stability of a class-difference equations. It is also shown that the proposed controller achieves semi-global stabilization of the system if its actuator is subject to either magnitude saturation or energy constraints under the condition that the open-loop system is only polynomially unstable. Numerical examples have been worked out to illustrate the effectiveness of the proposed approaches. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]