Cross-Term Forwarding for Systems With Time Delay

This paper presents a Lyapunov-based control design method for nonlinear systems with time delay. The key step is construction of a composite Lyapunov functional $V$ for a stable cascade. This functional consists of Lyapunov functionals for the subsystems and a cross-term defined by an infinite integral. The “$L_{g}V$-type” control law is then employed to achieve global asymptotic stability. The design procedure can be applied recursively to stabilize complex feedforward structures. When applied to a linear cascade, it gives a formula for the control law even if some parts of the system can only be stabilized through channels with multiple non-commensurate or distributed delays.      

Stabilization of Networked Control Systems With a New Delay Characterization

This paper presents a new approach to solving the problem of stabilization for networked control systems. Mean-square asymptotic stability is derived for the closed-loop networked control systems, and based on this, a controller design procedure is proposed for stabilization purpose. An inverted pendulum system is utilized to show the effectiveness and applicability of the proposed results.     

Stability Analysis and Stabilization for Discrete-Time Fuzzy Systems With Time-Varying Delay

This paper is concerned with the problems of stability analysis and stabilization for discrete-time Takagi–Sugeno fuzzy systems with time-varying state delay. By constructing a new fuzzy Lyapunov function and by making use of novel techniques, an improved delay-dependent stability condition is obtained, which is dependent on the lower and upper delay bounds. The merit of the proposed stability condition lies in its reduced conservatism, which is achieved by avoiding the utilization of some bounding inequalities for the cross products between two vectors. Then, a delay-dependent stabilization approach based on a parallel distributed compensation scheme is developed for both state feedback and observer-based output feedback cases. The proposed stability and stabilization conditions are formulated in terms of linear matrix inequalities, which can be solved efficiently by using existing optimization techniques. Two illustrative examples are provided to demonstrate the effectiveness of the results proposed in this paper.      

延迟时间未知的时延系统灰色预测控制

延迟时间的变化可能会引起控制品质的恶化,甚至使系统不稳定,利用灰色预测控制不需要掌握被控对象模型结构的先验信息,具有很强的自适应性的优点,同时利用神经网络辨识延识系统的延迟时间来在线调整灰色预测控制器的参数,将二结合用于有不确定性延迟时间的大延迟系统的控制,仿真结果表明这种控制策略具有很好的控制效果。它是大延迟控制中克服延迟时间变化的很有希望的方法。     

An Algorithm for Stabilization of Fractional-Order Time Delay Systems Using Fractional-Order PID Controllers

This technical note presents a solution to the problem of stabilizing a given fractional-order system with time delay using fractional-order Pl^lambdaD^mu controllers. It is based on determining a set of global stability regions in the (k_p, K_i, K_d)-space corresponding to the fractional orders lambda and mu in the range of (0, 2) and then choosing the biggest global stability region in this set. This method can be also used to find the set of stabilizing controllers that guarantees prespecified gain and phase margin requirements. The algorithm is simple and has reliable result which is illustrated by an example, and, hence, is practically useful in the analysis and design of fractional-order control systems.     

Stability Analysis and Design of Impulsive Control Systems With Time Delay

A class of impulsive control systems with time-varying delays is considered. By establishing an impulsive delay differential inequality, we analyze the global exponential stability of the impulsive delay systems and estimate the exponential convergence rate. On the basis of the analysis, a design procedure of impulsive controller is presented. The designed impulsive controller not only can globally exponentially stabilize the time delay systems, but also can control the exponential convergence rate of the systems. Two numerical examples are given to illustrate the effectiveness of the method.     

Linear Systems Subject to Input Saturation and Time Delay: Global Asymptotic Stabilization

This note deals with the problem of global asymptotic stabilization of linear systems by bounded static feedbacks subject to time delay. Under standard necessary conditions, we provide two constructions of controllers of nested saturation type which extends to the general case partial results of previous papers for arbitrary small bound on the control and large (constant) delay. To validate the approach, a third-order integrator and oscillator with multiplicity two example is presented     

Stabilization of second-order LTI switched systems

This paper studies and solves the problem of asymptotic stabilization of switched systems consisting of unstable secondorder linear time-invariant (LTI) subsystems. Necessary and sufficient conditions for asymptotic stabilizability are first obtained. If a switched system is asymptotically stabilizable, then the conic switching laws proposed in the paper are used to construct a switching law that asymptotically stabilizes the system. Switched systems consisting of two subsystems with unstable foci are studied first and then the results are extended to switched systems with unstable nodes and saddle points. The results are applicable to switched systems that consist of more than two subsystems.     

一类多时滞非线性系统的自适应鲁棒镇定

本文针对一类具有多时滞状态扰动的非线性系统,讨论了其自适应鲁棒镇定问题。在本文中,多时滞状态扰动的上界未知,通过设计自适应律估计上界的值。基于Lyapumov-Krasovskii函数设计了鲁棒控制器,使闭环系统的鲁棒镇定问题可解。一个数值例子的仿真验证了结论的正确性。     

Disturbance Decoupling of Time Delay Systems

A necessary and sufficient condition is derived for the solvability of the disturbance decoupling problem by a pure shift dynamic compensator. It corrects previously obtained results for multi‐input multi‐output (MIMO) systems. Also, necessary and sufficient conditions are given for the solvability of the problem by a dynamic compensator for single input single output (SISO) systems.     

New Approach to Delay-Dependent Stability Analysis and Stabilization for Continuous-Time Fuzzy Systems With Time-Varying Delay

This paper is concerned with delay-dependent stability analysis and stabilization problems for continuous-time Takagi and Sugeno (T-S) fuzzy systems with a time-varying delay. A new method for the delay-dependent stability analysis and stabilization is suggested, which is less conservative than other existing ones. First, based on a fuzzy Lyapunov-Krasovskii functional (LKF), a delay-dependent stability criterion is derived for the open-loop fuzzy systems. In the derivation process, some free fuzzy weighting matrices are introduced to express the relationships among the terms of the system equation, and among the terms in the Leibniz-Newton formula. Then, a delay-dependent stabilization condition based on the so-called parallel distributed compensation (PDC) scheme is worked out for the closed-loop fuzzy systems. The proposed stability criterion and stabilization condition are represented in terms of linear matrix inequalities (LMIs) and compared with the existing ones via two examples. Finally, application to control of a truck-trailer is also given to illustrate the effectiveness of the proposed design method.     

含有纯滞后系统的控制方法

针对时滞对象的控制问题,着重选取几种控制方法,考虑模型失配,时滞大小及干扰作用等因素,进行仿真,比较控制性能,以期对含有大时滞的实际对象的控制起到方法上的指导作用,结果表明,其中预测PI和内模PID两种控制方法响应速度快,超调量小,对模型失配的鲁棒性强,抗干扰能力好,时滞时间越长,越能体现出其优越性,是在克服纯滞后所产生影响的较好的控制方法。     

Memoryless State Feedback Controller Design for Time Delay Systems With Matched Uncertain Nonlinearities

The robust control problem for a class of uncertain time-delay systems is investigated. The systems include multiple time delays and uncertain nonlinear functions. To our best knowledge, no controller design method for the systems is reported in the literature except for sliding mode control (SMC). However, the sliding mode controller must use the delayed state of the system, so that the precise time delays have to be known, and also a large memory is needed for controller implementation. To overcome the shortcomings, we employ the backstepping method to design a memoryless state feedback controller. By constructing a novel Lyapunov-Krasovskii functional, we show that the resulting closed-loop system is asymptotically stable. Simulations are done to verify the effectiveness of the proposed method.     

Stabilization of Single‐Input LTI Systems by Proportional‐Derivative Feedback

This article presents an efficient solution to the stabilization pole placement problem for single‐input linear time‐invariant (LTI) systems by proportional‐derivative (PD) feedback. For a controllable system, any arbitrary closed‐loop poles can be placed in order to achieve the desired closed‐loop system performance. Its derivation is based on the transformation of linear system into Hessenberg form by a special coordinate transformation before solving the pole placement problem. The available degrees of freedom offered by PD feedback are utilized to obtain closed‐loop systems with small gains. So, the minimization problem for a suitably chosen cost function is formulated. Simulation results are included to show the effectiveness of the proposed approach.     

Adaptive Dynamic Surface Control for Stabilization of Parametric Strict-Feedback Nonlinear Systems With Unknown Time Delays

The robust stabilization method via the dynamic surface control (DSC) is proposed for uncertain nonlinear systems with unknown time delays in parametric strict-feedback form. That is, the DSC technique is extended to state time delay nonlinear systems with linear parametric uncertainties. The proposed control system can overcome not only the problem of ldquoexplosion of complexityrdquo inherent in the backstepping design method but also the uncertainties of the unknown time delays by choosing appropriate Lyapunov-Krasovskii functionals. In addition, we prove that all the signals in the closed-loop system are semiglobally uniformly bounded. Finally, an example is provided to illustrate the effectiveness of the proposed control system.     

模糊预测控制在时滞系统中的应用

几乎所有控制中都存在时滞,也叫死区时间,在此时间里,生产过程的实际值根本不会对控制器的调节作用起任何反应.时滞的存在会带来超调,震荡等诸多问题.测量方面有了时滞,控制器不能及时发现变量的变化,控制方面有了时滞,控制作用不能及时产生效应.本文结合模糊控制和模糊预测算法,预测控制量和输出量,减少了时滞,提高了控制质量.     

Passive Bilateral Teleoperation With Constant Time Delay

We propose a novel control framework for bilateral teleoperation of a pair of multi-degree-of-freedom nonlinear robotic systems under constant communication delays. The proposed framework uses the simple proportional-derivative control, i.e., the master and slave robots are directly connected via spring and damper over the delayed communication channels. Using the controller passivity concept, the Lyapunov–Krasovskii technique, and Parseval's identity, we can passify the combination of the delayed communication and control blocks altogether robustly, as long as the delays are finite constants and an upper bound for the round-trip delay is known. Having explicit position feedback through the delayed P-action, the proposed framework enforces master–slave position coordination, which is often compromised in the conventional scattering-based teleoperation. The proposed control framework provides humans with extended physiological proprioception, so that s/he can affect and sense the remote slave environments mainly relying on her/his musculoskeletal systems. Simulation and experiments are performed to validate and highlight properties of the proposed control framework.     

Stability and Stabilization of Two‐Dimensional LTI Switched Systems with Potentially Unstable Focus

This paper investigates stability and stabilization of two‐dimensional switched linear time‐invariant (LTI) systems with potentially unstable focus. For the case that the origin is a single common focus of all subsystems, we first give continuous positive definite functions related only to the elements of subsystems' state matrices. Then, based on the continuous positive definite functions obtained, this paper proposes several sufficient conditions of stability/asymptotic stability/instability of the kind of switched LTI systems. By means of the stability results proposed, global asymptotic stabilizing controls (GASC), global asymptotic stabilizing switching paths (GASSP) and corresponding algorithms are designed for two‐dimensional switched LTI systems with focus. Finally, two illustrative examples and numerical simulations demonstrate the effectiveness of the new stability and stabilization results obtained in this paper.     

Delay-dependent Robust Singular Systems Stabilization for Uncertain with State Delay

This paper considers the problem of delay-dependent robust stabilization for uncertain singular delay systems. In terms of linear matrix inequality （LMI） approach, a delay-dependent stability criterion is given to ensure that the nominal system is regular, impulse free, and stable. Based on the criterion, the problem is solved via state feedback controller, which guarantees that the resultant closed-loop system is regular, impulse free, and stable for all admissible uncertainties. An explicit expression for the desired controller is also given. Some numerical examples are provided to illustrate the validity of the proposed methods.     

线性不确定时滞系统的时滞依赖鲁棒镇定方法研究

研究一类同时存在状态和控制滞后的线性不确定时滞系统的鲁棒镇定问题。系统的不确定项参数时为未知但范数有界,其滞后项也时时变的。对此,给出一个使得系统鲁棒稳定的无记忆状态反馈控制律,所得结果与时滞相关,且相应的结果以线性矩阵不等式的形式给出。