New results on dynamic output state feedback stabilization of some class of time-varying nonlinear Caputo derivative systems

This study deals with the model, exponential stability and controller design problems of singular networked control system (NCS). Two new control methods of dynamical state feedback control and dynamical state feedback proportional-integral (PI) control for the NCS with time-delay and data packet dropout are addressed. Using two new control methods, the singular NCS is modeled as an asynchronous dynamical system (ADS) constrained by event rates. Furthermore, based on the ADS theory, principle of Lyapunov stability and method of linear matrix inequality, the semi-negative definite matrix conditions of exponential stability, the dynamical state feedback controller and the dynamical state feedback PI controller design for the NCS are given. Finally, numerical examples illustrate the feasibility of the proposed control methods of dynamical state feedback control and dynamical state feedback PI control, semi-negative definite matrix conditions of exponential stability and the controller design.

This study deals with the exponential stability of singular networked control system (NCS) with time-delay and data packet dropout. Two new control methods of dynamical state feedback control and dynamical state feedback proportional-integral (PI) control for the singular NCS are addressed. The singular NCS with time-delay and data packet dropout is modeled as an asynchronous dynamical system (ADS) constrained by event rates. Furthermore, based on the ADS theory, principle of Lyapunov stability and method of linear matrix inequality, the semi-negative definite matrix conditions of exponential stability, the dynamical state feedback controller and the dynamical state feedback PI controller design for the NCS are given. Finally, numerical examples illustrate the feasibility of the proposed control methods of dynamical state feedback control and dynamical state feedback PI control, semi-negative definite matrix conditions of exponential stability and the controller design.

Global state regulation of time-delay minimum-phase systems by delay-free dynamic compensation

The paper focuses on the problem of nonfragile fuzzy dynamic output feedback control for continuous‐time nonlinear systems. This study aims to develop a method for nonfragile dynamic output feedback control with multiplicative gain uncertainty, ensuring that the closed‐loop system meets the performance and guarantees stability. To address the issue of the integral Lyapunov function, the matrix decoupling technique is proposed. In addition, combined with the Takagi‐Sugeno fuzzy model, the relevant linear matrix inequality based on the multiplicative nonfragile dynamic feedback controller was obtained. Finally, the performance of the proposed technique is substantiated via two separate simulation examples.

This paper presents a dynamic feedback framework for the control of time-delay cascade systems with unstable zero dynamics. Both dynamic state and output feedback control strategies are studied. Recognizing the difficulty of controlling time-delay systems via static feedback, we develop a systematic method, by taking advantage of dynamic feedback, for the design of delay-free, dynamic state and output feedback compensators that achieve global state regulation with stability. The controlled plants under consideration not only cover time-delay nonlinear systems in the normal form, but also include a class of time-delay cascade systems beyond the normal form. In the case of state feedback, the zero dynamics are not required to be "minimum phase" but satisfy certain regularity conditions. In the output feedback case, appropriate conditions are characterized for the zero dynamics so that the existence of a dynamic output controller is ensured. A key feature of the proposed control strategies is the utilization of dynamic gains to counteract the effect of time-delay nonlinearities and unstable zero dynamics.

In this paper, we consider the cooperative output regulation of linear multi-agent systems under switching network. The problem can be viewed as a generalization of the leader-following consensus problem of multi-agent systems. Due to the limited information exchanges of different subsystems, the problem cannot be solved by the decentralized approach and is not allowed to be solved by the centralized control. By devising a distributed observer network, we can solve the problem by both dynamic state feedback control and dynamic measurement output feedback control. As an application of our main result, we show that a special case of our results leads to the solution of the leader-following consensus problem of linear multi-agent systems.

This paper presents dynamic output feedback control designs for discrete Takagi-Sugeno fuzzy systems. A dynamic output feedback controller is constructed based on the concept of dynamic parallel distributed compensation (DPDC). Design conditions for optimal dynamic feedback control are obtained in terms of linear matrix inequalities (LMIs). In application to a vehicle with triple trailers setup, we utilize the optimal design conditions to avoid the jack-knife phenomenon. Our results demonstrate that the optimal dynamic output feedback design effectively achieves the backing up control of the vehicle with triple trailers while avoiding the jackknife phenomenon. More importantly, we demonstrate that the designed optimal control can achieve the backing up control without two potentiometers that were employed to measure the relative angles (of a vehicle with triple trailers) in our previous experiments.

Most of the complex industrial plants are generally interacting multi-input multi-output (MIMO) systems. Controller design for such complex plants is a challenging task. In this paper, design of eigenstructure assignment (EA)-based multi-objective dynamic state and output feedback controllers for linear discrete MIMO system are considered. The significance of parametric eigenstructure assignment technique is that it provides more design degrees of freedom to obtain multi-objective functions. Based on parametric eigenstructure assignment, control problem is formulated to achieve conflicting multi-objective functions such as robust stability to parameter perturbation and smaller control gain to improve the transient response of the closed loop system. It is difficult to solve the conflicting objective functions using conventional optimisation techniques. In this paper, fast and elitist multi-objective evolutionary algorithm (MOEA) known as non-dominated sorting genetic algorithm-II (NSGA-II) is successfully applied for solving multi-objective problem. The robust stability and transient response are ensured by minimum condition number of eigenvector and minimum norm of controller gain. The proposed controllers use complex valued chromosomes to represent complex parametric vector. The effectiveness of the proposed controllers is validated by implementing the same in an interacting three-tank benchmark system.

In this paper, we study the robust output regulation problem for linear systems with input time-delay. By extending the internal model design method to linear time-delay systems, we have established solvability conditions for the problem by both dynamic state feedback control and dynamic output feedback control. The advantages of internal model approach over the feedforward design approach are that it can handle perturbations of the uncertain parameters in the plant and the control law, and it does not need to solve the regulator equations.

This paper investigates the design problem of constructing the state and output feedback stabilisation controller for a class of uncertain nonlinear systems subject to time-delay. First, a dynamic linear state feedback control law with an adaptive strategy is developed to globally stabilise the uncertain nonlinear time-delay system under a lower-triangular higher-order growth condition. Then, one more challenging problem of the adaptive output feedback stabilisation is addressed, which can globally stabilise the time-delay system when the unmeasurable states linearly grow with rate functions consisting of higher-order output.

Smooth dynamic output feedback control for multiple time-delay systems with nonlinear uncertainties

In this technical note, we consider the cooperative output regulation problem for linear multi-agent systems subject to communication delays and switching networks by a distributed feedforward approach. Both distributed dynamic state feedback controller and distributed dynamic measurement output feedback controller are proposed to solve the problem. In comparison with the existing result for the similar problem, our result can handle the cooperative output regulation problem subject to nonuniform time-varying communication delays and jointly connected switching communication networks. As an application of cooperative output regulation, it is shown that our main result can solve the leader-following consensus problem and includes some existing results as its special cases.

Cooperative output regulation problem for linear time-delay multi-agent systems under switching network

This paper is concerned with the event-triggered dynamic output feedback control for linear time invariant (LTI) systems subject to actuator saturation. Firstly, a novel event-triggered scheme and dynamic output feedback controller are presented. Under the proposed framework: (a) the samplings of the sensor are designed as specific time-varying signals utilizing exponentially decaying function; (b) the dynamic feedback controller is equipped with an anti-windup compensator; (c) a lower bound of the inter-event interval is derived to exclude the Zeno behavior. Secondly, by constructing Lyapunov function and generally sector condition, some sufficient stability criteria are derived via linear matrix inequalities. Thirdly, depend on the stability criteria and MATLAB LMI toolbox, the parameters of event-triggered scheme and the controller are calculated. Finally, the effectiveness of the proposed method is illustrated by a numerical example.

A dynamic output feedback regulator design which cascades an observer with a dynamic state feedback control law is presented. A comparison is made with the usual regulator design in which an observer is cascaded with a proportional state feedback gain. It is shown that under certain conditions both approaches can lead to the same output feedback system. However, a comparison of the output feedback response with the responses of the two state feedback Bystems (dynamic state feedback and proportional state feedback) shows that the norm of the difference between the output feedback response and the set of dynamic state feedback responses is never greater than the norm of the difference between the output feedback response and the proportional feedback response. In practice this means that the set of possible responses with dynamic state feedback provides a good indication of the actual responses which will be achieved with output feedback (dynamic state feedback law plus observer). With the proposed design scheme the system transient response can therefore be approximately analysed using the state feedback system alone before the observer is designed. The control law and observer design problems ore therefore more completely decoupled than they are in the typical proportional gain plus observer approach.