Operator-based nonlinear feedback control design using robust right coprime factorization

In this note, robust stabilization and tracking performance of operator based nonlinear feedback control systems are studied by using robust right coprime factorization. Specifically, a new condition of robust right coprime factorization of nonlinear systems with unknown bounded perturbations is derived. Using the new condition, a broader class of nonlinear plants can be controlled robustly. When the spaces of the nonlinear plant output and the reference input are different, a space change filter is designed, and in this case this note considers tracking controller design using the exponential iteration theorem.     

Operator-based robust nonlinear control system design for MIMO nonlinear plants with unknown coupling effects

In this article, operator-based robust nonlinear control system design for multi-input multi-output (MIMO) plants with unknown coupling effects is considered. That is, by using operator-based robust nonlinear control design, coupling effects existing in the MIMO nonlinear plants can be decoupled based on a feedback design and robust right coprime factorisation approach, the coupling effects caused by controllers and plant outputs can be stabilised by using definition of Lipschitz operator and contraction mapping theorem, and output tracking performance can be realised by a tracking design scheme. Finally, a simulation example about temperature control process of 3-input/3-output aluminum plate is given to support the theoretical analysis.     

不确定时变时滞系统的自适应全局鲁棒滑模控制

针对一类存在时变状态时滞的不确定性系统, 基于全程滑模的思想, 引入一种带状态时滞项的积分型滑模面, 以消除趋近模态, 实现全程滑模控制; 基于一种新颖的自由权矩阵时滞转换模型, 采用线性矩阵不等式(LMI) 的方法给出并证明了滑动模态稳定的充分条件, 降低了保守性; 结合自适应控制思想设计出自适应滑模控制器, 克服了不确定性以及时变的时滞影响.

     

Stability and robust stability for systems with a time-varying delay

To concern the stability and robust stability criteria for systems with time-varying delays, this note uses not only the time-varying-delayed state x(t-h(t)) but also the delay-upper-bounded state to exploit all possible information for the relationship among a current state x(t), an exactly delayed state x(t-h(t)), a marginally delayed state , and the derivative of the state , when constructing Lyapunov-Krasovskii functionals and some appropriate integral inequalities, originally suggested by Park (1999. A delay-dependent stability criterion for systems with uncertain time-invariant delays. IEEE Transactions on Automatic Control, 44(4), 876-877). Two fundamental criteria are provided for the cases where no bound of delay derivative is assumed and where an upper bound of delay derivative is assumed. Examples show the resulting criteria outperform all existing ones in the literature.     

Operator-based robust control for nonlinear uncertain systems with unknown backlash-like hysteresis

In this paper, operator based robust control for nonlinear uncertain system with unknown backlash-like hysteresis is considered. In detail, a continuous backlash-like hysteresis operator is proved to be corresponding to a one-to-one operator, that is, it is suitable to be used in operator theoretic based control theory. Moreover, an internal model control (IMC) structure with one parallel compensating operator is proposed for nonlinear uncertain system with unknown backlash-like hysteresis. Based on the proposed control scheme, the designed system is robustly stable and the desired output tracking performance can be realized simultaneously. Finally, a simulation example about nonlinear plant preceded by backlash is given to show the design procedure of the proposed method.     

Delay-dependent robust observer-based control for discrete-time uncertain singular systems with interval time-varying state delay

The problem of observer-based robust control design is studied for discrete-time singular systems with norm-bounded uncertainties and a time-varying delay. More precisely, a delay-dependent criterion is established that guarantees the admissibility of the considered systems, without resorting to its decomposition. Based on the proposed criterion and without the assumption that the considered systems are admissible, robust observer-based controllers are designed for discrete-time singular time-delay systems such that the closed-loop systems have the characteristics of regularity, causality and asymptotic stability. Seeking computational convenience, all the developed results are cast in the format of strict linear matrix inequalities (LMIs). Finally, some numerical examples are presented to show the feasibility of the proposed approach.     

Observer-based robust stabilization for uncertain systems with unknown time-varying delay

This paper focuses on the problem of robust stabilization for a class of linear systems with uncertain parameters and time varying delays in states. The parameter uncertainty is continuous, time varying, and norm-bounded. The state delay is unknown and time varying. The states of the system are not all measurable and an observer is constructed to estimate the states. If a linear matrix inequality (LMI) is solvable, the gains of the controller and observer can be obtained from the solution of the LMI. The observer and controller are dependent on the size of time delay and on the size of delay derivative. Finally, an example is given to illustrate the effectiveness of the proposed control method.     

Comments on a robust model reference adaptive control for non-minimum phase systems with unknown or time-varying delay

In the above paper Makoudi and Radouane, 2000 [A robust model reference adaptive control for non-minimum phase systems with unknown or time-varying delay. Automatica, 36, 1057-1065.], a model reference adaptive control (MRAC) algorithm is presented for non-minimum phase systems with unknown or time-varying delays. Unfortunately, this paper contains several mathematical mistakes that render the proofs of the claimed results erroneous. Furthermore, there are no obvious ways to correct these errors, so that the results presented in this paper are questionable.     

Robust control for nonlinear time-varying systems with application to a robotic manipulator

Sliding mode control methods have been used widely because they provide robustness against parameter variations and disturbances. This paper focuses on the problem of a robust output-sliding control design for a class of nonlinear time-varying systems. Output signals are used for the switching function definition. The control law formulation is emphasized. Input and output linearization is used. Output tracking can be achieved against a class of time-varying parameter variations and external disturbances. An application to a two-degree-of-freedom manipulator indicates that the proposed switching control law drives the system state trajectories onto the chosen sliding mode in finite time and the output tracking is guaranteed.     

中立型变时滞系统的鲁棒稳定性

考虑不确定中立型变时滞系统的鲁棒稳定性问题. 首先, 引入新的变量来代替系统的不确定性; 然后, 通过构造一般形式的Lyapunov-Krasovskii泛函、使用积分不等式并引入自由矩阵, 得到了基于线性矩阵不等式的系统稳定性判据. 该结论与中立型时滞, 离散时滞及其导数均相关, 具有较小的保守性. 最后, 通过仿真算例说明了所得到的结论在保守性上优于现存的结果以及中立型时滞, 离散时滞及其导数三者之间的关系.     

Delay-dependent robust stability for uncertain linear systems with interval time-varying delay

This paper is concerned with the delay-dependent robust stability problem for uncertain linear systems with interval time-varying delay. The time-varying delay is assumed to belong to an interval and no restriction on the derivative of the time-varying delay is needed, which allows the delay to be a fast time-varying function. The uncertainty under consideration is norm-bounded, and possibly time-varying, uncertainty. Based on the Lyapunov-Krasovskii functional approach, a stability criterion is derived by introducing some relaxation matrices that can be used to reduce the conservatism of the criteria. Numerical examples are given to demonstrate effectiveness of the proposed method.     

Delay-dependent criteria for the robust stability of systems with time-varying delay

The problem of delay-dependent robust stability for systems with time-varying delay has been considered. By using the S-procedure and the Park's inequality in the recent issue, a delay-dependent robust stability criterion which is less conservative than the previous results has been derived for time-delay systems with time-varying structured uncertainties. The same idea has also been easily extended to the systems with nonlinear perturbations. Numerical examples illustrated the effectiveness and the improvement of the proposed approach.     

Delay-dependent criteria for robust stability of time-varying delay systems

This paper deals with the problem of delay-dependent robust stability for systems with time-varying structured uncertainties and time-varying delays. Some new delay-dependent stability criteria are devised by taking the relationship between the terms in the Leibniz-Newton formula into account. Since free weighting matrices are used to express this relationship and since appropriate ones are selected by means of linear matrix inequalities, the new criteria are less conservative than existing ones. Numerical examples suggest that the proposed criteria are effective and are an improvement over previous ones.     

带有干扰的线性时变系统的非线性鲁棒控制

研究了含有未知时变参数和有界干扰的单输入单输出线性时变系统的鲁棒控制问题.系统时变参数只要求光滑有界而不限制为慢时变或参数上界已知.利用时变的状态变换得到新的动态系统,基于Backstepping方法,设计出一种非线性鲁棒控制器.通过适当选择控制器参数,可以保证闭环系统是全局渐近稳定的.仿真例子表明了算法的有效性.     

New robust exponential stability analysis for uncertain neural networks with time-varying delay

In this paper, the global robust exponential stability is considered for a class of neural networks with parametric uncer-tainties and time-varying delay. By using Lyapunov functional method, and by resorting to the new technique for estimating the upper bound of the derivative of the Lyapunov functional, some less conservative exponential stability criteria are derived in terms of linear matrix inequalities (LMIs). Numerical examples are presented to show the effectiveness of the proposed method.     

含区间时变时滞的线性不确定系统鲁棒稳定性新判据

研究一类区间时变时滞线性不确定系统的鲁棒稳定性问题.通过引入增广Lyapunov泛函,结合积分不等式方法,导出了区间时变时滞线性系统的时滞相关鲁棒稳定性新判据.与现有方法不同,该方法不涉及自由权矩阵技术和任何模型变换,减少了理论和计算上的复杂性,而且在估计Lyapunov泛函导数的上界时没有忽略某些有用项.数值算例表明,所提出的判据是有效的,具有更低的保守性.     

Delay-dependent robust H-infinity filtering for uncertain linear systems with time-varying interval delay

This paper proposed a design method for delay-dependent robust H-infinity filter of linear systems with uncertainty and time-varying interval delay.The proposed method was shown to be much simpler than existing ones while giving significant improvement to the existing results.The key step in the method was to construct a special type of Lyapunov functional for the filter design problem.Unlike the existing techniques,the proposed method employed neither free weighting matrices nor any model transformation,le...     

Fault estimator design for a class of switched systems with time-varying delay

This article studies the problem of fault estimator design for switched time-delay systems with impulsive control. The delay signal is assumed to be uniformly bounded, differentiable and has a bounded derivative. The problem is first formulated in the framework of H _∞ filtering by incorporating a priori knowledge of the fault into the design procedure. A hybrid controller, composed of a fault estimator and an impulsive controller, is constructed. Some delay-dependent sufficient conditions are derived on the existence of the hybrid controller by using the multiple Lyapunov functional approach. In addition, based on the cone complementarity algorithm, the solutions to the parameter matrices are obtained by solving a set of linear matrix inequalities. Finally, a numerical example is given to illustrate the effectiveness of the proposed approach.     

Delay dependent robust stability of singular systems with time-varying delay

This paper deals with the problem of robust stability of uncertain singular continuous systems with time-varying delays. The parametric uncertainties are assumed to be norm bounded. Delay dependent conditions are given to ensure that the uncertain singular system is regular, impulse free, and stable for all admissible uncertainties. The results are given in terms of linear matrix inequalities (LMIs). Finally, numerical examples are provided to illustrate the effectiveness of the proposed method, and to compare with previous works.     

On control for linear systems with interval time-varying delay

This paper deals with the problem of delay-dependent robust H_∞ control for linear time-delay systems with norm-bounded, and possibly time-varying, uncertainty. The time-delay is assumed to be a time-varying continuous function belonging to a given interval, which means that the lower and upper bounds for the time-varying delay are available, and no restriction on the derivative of the time-varying delay is needed, which allows the time-delay to be a fast time-varying function. Based on an integral inequality, which is introduced in this paper, and Lyapunov–Krasovskii functional approach, a delay-dependent bounded real lemma (BRL) is first established without using model transformation and bounding techniques on the related cross product terms. Then employing the obtained BRL, a delay-dependent condition for the existence of a state feedback controller, which ensures asymptotic stability and a prescribed H_∞ performance level of the closed-loop systems for all admissible uncertainties, is proposed in terms of a linear matrix inequality (LMI). A numerical example is also given to illustrate the effectiveness of the proposed method.