Exponential stability of a class of nonlinear dynamical systems with uncertainties

Exponential stability for a class of nonlinear dynamical systems with uncertainties is investigated. Based on the stability of the nominal systems, a new approach to synthesizing a class of continuous state feedback controllers for uncertain nonlinear dynamical systems is proposed. By such a class of feedback controllers, we can guarantee exponential stability of uncertain nonlinear dynamical systems. Our approach can give a clear insight into system analysis. Finally, an illustrative example is given to demonstrate the utilization of the approach developed in this paper.     

Guaranteed cost observer-based control of uncertain time-lag systems

This paper investigates the design of robust observer-based controllers for a class of uncertain linear time-lag systems. The uncertainties are assumed to be norm-bounded. We extend the previous results on quadratic-cost control to the case of observer-based control for uncertain systems with unknown state and input time-lags. By introducing an appropriate definition of quadratic stability for uncertain time-lag systems, it is shown that observer-based controllers can be constructed via solutions of linear-matrix inequalities. A simulation example is given to illustrate the theoretical developments.     

Trajectory-based design of robust non-fragile controllers for a class of uncertain linear continuous-time systems

This paper deals with a design problem of robust non-fragile stabilizing controllers for a class of uncertain linear continuous-time systems. The proposed design approach of robust non-fragile controllers is based on computation of the trajectory for the uncertain linear system and differs from the existing methods based on quadratic stabilization via Lyapunov criterion. In this paper, we show that sufficient conditions for asymptotical stability of the linear system with uncertainties and controller gain variations, and a LMI-based design algorithm of a robust non-fragile controller. Furthermore, we extend the result to the design problem of decentralized robust non-fragile controllers for a class of uncertain large-scale interconnected systems. Finally, the effectiveness of the proposed design scheme of robust non-fragile controllers is shown through illustrative examples.     

Stability analysis of fuzzy control systems subject to uncertain grades of membership.

This paper presents relaxed stability conditions for fuzzy control systems subject to parameter uncertainties. As the parameter uncertainties introduce uncertain grades of membership to the fuzzy control systems, the favorable property offered by sharing the same premises in the fuzzy plant models and fuzzy controllers cannot be employed to enhance the stabilization ability of the fuzzy control systems. To widen the applicability of the fuzzy control approach, fuzzy control systems subject to uncertain grades of membership will be investigated. New relaxed stability conditions will be derived to guarantee the stability of this class of fuzzy control systems. A numerical example will be given to show the effectiveness of the proposed approach.     

一类具有Markov跳跃参数的不确定线性跳跃系统鲁棒非脆弱H∞控制问题研究

This paper describes the synthesis of robust and non-fragile H∞ state feedback controllers for a class of uncertain jump linear systems with Markovian jumping parameters and state multiplicative noises. Under the assumption of a complete access to the norm-bounds of the system uncertainties and controller gain variations, sufficient conditions on the existence of robust stochastic stability and γ-disturbanee attenuation H∞ property are presented. A key feature of this scheme is that the gain matrices of controller are only based on lt, the observed projection of the current regime rt.     

Estimation of the asymptotic stability region of uncertain systemswith bounded sliding mode controllers

In this note, the problem of estimating the asymptotic stability region (ASR) of uncertain systems with bounded sliding mode controllers is considered. To simplify the problem the authors use a state transformation and choose a suitable Lyapunov function for the transformed control system. Using the Lyapunov function the authors estimate the ASR and show the exponential stability of the closed-loop control system in the region. Also, by an example the authors show that for a certain class of uncertain dynamical systems with bounded sliding mode controllers their method gives a more improved estimate of the ASR     

不确定时滞系统的鲁棒绝对稳定性研究

基于Lyapunov稳定性理论，采用线性矩阵不等式处理方法，研究具有参数不确定性的时滞系统鲁棒绝对稳定性问题．导出了用线性矩阵不等式系统可行性描述的系统鲁棒绝对稳定的滞后依赖型条件，据此可计算出最大的允许时滞界．通过求解一组线性矩阵不等式，给出使得闭环系统鲁棒绝对稳定的无记忆状态反馈控制律设计方法。     

Robust output tracking of nonlinear systems with mismatched uncertainties

The problem of robust output tracking for a class of uncertain nonlinear systems which do not satisfy the conventional matching condition is considered. The main assumption on the uncertainty is that the triangularity condition is satisfied. Based on backstepping method and input/output linearization approach, we propose a class of non-adaptive state feedback controllers which can guarantee exponential stability of the tracking error for the uncertain nonlinear systems first. Next, adaptive control laws are developed so that no prior knowledge of the bounds on the uncertainties is required. By updating these upper bounds, we design a class of adaptive robust controllers. It is shown that under the proposed adaptive robust control the tracking error of the controlled system converges to zero as time approaches infinity.     

New Robust Stability Conditions and Design of Robust Stabilizing Controllers for Takagi–Sugeno Fuzzy Time-Delay Systems

In this paper, we consider robust stability and stabilization of uncertain Takagi-Sugeno fuzzy time-delay systems where uncertainties come into the state and input matrices. Some stability conditions and robust stability conditions for fuzzy time-delay systems have already been obtained in the literature. However, those conditions are rather conservative and do not guarantee the stability of a wide class of fuzzy systems. This is true in case of designing stabilizing controllers for fuzzy time-delay systems and it thus leads to a conservative fuzzy controller design as well. We first consider rather relaxed robust stability conditions of uncertain fuzzy systems. To this end, we introduce an auxiliary system to the original fuzzy time-delay system to obtain generalized delay-dependent stability conditions. Such an auxiliary system has some arbitrary matrices that generalize not only the system representation but also delay-dependent stability conditions. Conditions we obtain here are delay-dependent conditions that depend on the upper bound of time-delay, and are given in terms of linear matrix inequalities (LMIs). Then, we compare our delay-dependent stability conditions with other conditions in the literature, and show that our conditions guarantee the stability of a wider class of systems than others. Next, we consider the robust stabilization problem with memoryless and delayed state feedback controllers. Based on our generalized robust stability conditions, we obtain delay-dependent sufficient conditions for the closed-loop system to be robustly stable, and give a design method of robustly stabilizing controllers. Finally, we give three examples that illustrate our results.     

Globally robust nonlinear PID controllers for robot manipulators with an uncertain Jacobian matrix

Based on a continuous piecewise-differentiable increasing functions vector, a class of robust nonlinear PID (RN-PID) controllers is proposed for setpoint control with uncertain Jacobian matrix. Globally asymptotic stability is guaranteed and only position and joint velocity measurements are required. And stability problem arising from integral action and integrator windup, are consequently resolved. Furthemnore, RN-PID controllers can be of effective alternative for anti-integrator-wind-up,the control performance would not be very bad in the presence of rough parameter tuning.     

Robust output feedback stabilization of uncertain dynamic systems with bounded controllers

We propose a new class of infinitely many bounded output feedback controllers for uncertain dynamic systems with bounded uncertainties. No statistical information about the uncertainties is assumed. A variable structure systems approach is employed in the synthesis of the proposed output feedback controllers. The role of the system zeros in the output feedback stabilization using the variable structure approach is discussed. We show that the proposed controllers guarantee the practical stability of the closed-loop system and give estimates of the regions of practical stability.     

Robust control for a class of uncertain switched fuzzy systems

A model of uncertain switched fuzzy systems whose subsystems are uncertain fuzzy systems is presented. Robust controllers for a class of switched fuzzy systems are designed by using the Lyapunov function method. Stability conditions for global asymptotic stability are developed and a switching strategy is proposed. An example shows the effectiveness of the method.     

基于单位分解的一类非线性不确定系统跟踪控制设计

利用单位分解在紧致域上能够以任意给定精度逼近连续函数的性质,针对一类不确定非线性系统设计了带有自适应律的鲁棒自适应跟踪控制器．结果表明这种控制器可以使输出跟踪误差渐近收敛到零点的一个小邻域内,并保证闭环系统的所有状态一致有界．最后的仿真实例说明了该方法的有效性．     

Adaptive backstepping control of a class of uncertain nonlinear systems with unknown backlash-like hysteresis

In this note, we consider the same class of systems as in a previous paper, i.e., a class of uncertain dynamic nonlinear systems preceded by unknown backlash-like hysteresis nonlinearities, where the hysteresis is modeled by a differential equation, in the presence of bounded external disturbances. By using backstepping technique, robust adaptive backstepping control algorithms are developed. Unlike some existing control schemes for systems with hysteresis, the developed backstepping controllers do not require the uncertain parameters within known intervals. Also, no knowledge is assumed on the bound of the "disturbance-like" term, a combination of the external disturbances and a term separated from the hysteresis model. It is shown that the proposed controllers not only can guarantee global stability, but also transient performance.     

基于LMI 的不确定随机系统输出反馈保性能控制

针对一类不确定连续随机系统,研究了具有输出反馈控制器的保性能控制．首先,对于范数有界 的不确定随机系统,得到了具有输出反馈控制器的闭环系统的二次型性能指标的上界一般形式．其次,应用 线性矩阵不等式技术,研究了其闭环系统的二次稳定和二次保性能稳定;并且依据线性矩阵不等式优化方法, 得到了使闭环系统渐近稳定的最优输出反馈保性能控制器．最后,给出仿真算例,验证本文方法的可行性和 有效性．     

Adaptive robust control of uncertain nonlinear systems with nonlinear delayed state perturbations

The problem of robust stabilization of uncertain nonlinear dynamical systems with multiple time delays is considered. In the paper, the upper bound of the nonlinearity and uncertainty, including delayed states, is assumed to be a linear function of some parameters which are still assumed to be unknown. Here, we do not require that the nonlinear terms including delayed states are linear norm-bounded in the states. An improved adaptation law with σ-modification is employed to estimate the unknown parameters, and a class of memoryless adaptive robust state feedback controllers is proposed. It is also shown that the proposed adaptive robust controllers can guarantee the uniform asymptotic stability of uncertain nonlinear time-delay systems. Finally, as a numerical example, an uncertain time-delay ecosystem with two competing species is given to demonstrate the validity of the results.     

Exponential stability and stabilization of uncertain linear time-varying systems using parameter dependent Lyapunov function

In this paper, the problem of exponential stability and stabilization for a class of uncertain linear time-varying systems is considered. The system matrix belongs to a polytope and the time-varying parameter as well as its time derivative are bounded. Based on a time-varying version of Lyapunov stability theorem, new sufficient conditions for the exponential stability and stabilization via parameter dependent state feedback controllers (i.e., a gain scheduling controllers) are given. Using parameter dependent Lyapunov function, the conditions are formulated in terms of two linear matrix inequalities without introducing extra useless decision variables and hence are simply verified. The results are illustrated by numerical examples.     

类Lyapunov理论在类人形机器人任务空间内跟踪的应用

考虑了类人形机器人的各种不确定因素,提出了其手臂控制的新方法.基于类Lyapunov方法,设计出具有鲁棒性功能的任务空间控制器.该方法得到的控制器不但在有限确定时间内达到稳定跟踪,而且不需要雅可比矩阵求逆,对一定类型的外部干扰具有鲁棒性功能.最后通过数值仿真显示了所得结果的有效性及其应用方法.     

一类离散时间切换混杂系统鲁棒控制

由于切换规则的存在使得切换混杂控制系统的稳定性研究变得极为复杂,如何针对给定的系统设计适当的控制器和切换规则没有统一的方法.本文考虑一类线性不确定离散时间切换混杂系统的鲁棒二次镇定和渐近镇定问题.利用公共李雅普诺夫函数方法和多李雅普诺夫函数方法,分别设计了切换混杂系统鲁棒状态反馈控制器和鲁棒输出反馈控制器,保证了切换混杂系统的二次稳定性和渐近稳定性.仿真结果验证了所提算法的正确有效性.