不确定Lur'e时滞系统的鲁棒控制研究
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摘要
Lur’e系统是一类典型的非线性系统，其非线性项被约束在有限的或无限的霍尔维茨角域里。在实际的Lur’e控制系统中，不可避免地要遇到各种不确定性，诸如未建模动态、结构性的参数不确定性、工作环境的变化、降阶及线性化近似以及外部干扰的不确定性等。一般这些不确定性并非不可度量的，通常能给出这些不确定性大小的某种约束，鲁棒控制理论正是处理系统模型具有不确定性的有效方法。另一方面，在大多数维数很大的实际系统中，都有呈现奇异摄动特性的快变变量，如电力系统，冷轧机的工业控制系统，生物化学过程，核反应堆，飞机和火箭系统，以及化学扩散反应等。因此奇异系统的鲁棒控制研究也成了控制理论研究的热点之一。而且，由于大惯性环节、传输过程以及复杂的在线分析仪等不可避免地会导致滞后现象的产生，这些滞后特性往往会严重影响控制系统的稳定性以及系统的性能指标。所有以上这些现象在实际的控制系统中的存在，使得不确定Lur’e时滞系统的鲁棒控制问题的研究成为了必然。
本文研究了不确定Lur’e时滞系统的鲁棒控制问题，研究思路从系统状态的完全性以及状态的不完全性两方面入手。针对完全状态系统，采用LyapunovRazumikhin稳定性理论以及凸优化等重要理论，以线性矩阵不等式作为研究的工具，研究了鲁棒稳定性、鲁棒控制器的设计问题；针对不完全状态(奇异)系统，基于Barbalat引理以及非奇异线性降阶变换，研究了奇异系统的鲁棒稳定性、鲁棒控制器的设计问题。主要研究内容包括如下的几个方面：
1、通过采用一种新的状态变换，提出了一类不确定Lur’e时滞系统时滞依赖的鲁棒稳定及鲁棒二次镇定的新方法，得出的结果与已有的文献相比，保守性有明显地降低。
2、讨论了具有马尔科夫过程的不确定Lur’e跳变系统的鲁棒稳定及鲁棒H_∞控制问题，得到了基于线性矩阵不等式的保证闭环系统鲁棒稳定的充分条件，设计了鲁棒H_∞输出反馈控制器。
3、针对一类具有凸参数不确定性的Lur’e时滞系统，研究了当执行器与传感器分别出现故障的时候的可靠控制问题，得出了可靠H_∞控制器的设计方法。
4、针对一类不确定Lur’e奇异时滞系统，基于Barbalat引理以及非奇异降阶变换，讨论了Lur’e奇异时滞系统的鲁棒稳定问题，提出了鲁棒H_∞状态
浙江大学博士学位论文
反馈控制器的设计方法。
5、针对一类具有饱和执行器的不确定Lur’e奇异系统，提出了时滞依赖的鲁
棒稳定与鲁棒二次镇定的充分条件，所的结果不需要参数的整定。
6、针对任意协方差有界的有色噪声，讨论了一类不确定Lur’e奇异系统的鲁
棒凡滤波问题，得出了鲁棒几滤波器设计的充分条件。
7、针对一类不确定Lur’e时滞系统，通过线性变换，把它转换成奇异系统，
根据奇异系统鲁棒控制理论所得出的鲁棒稳定与鲁棒镇定控制器设计的
充分条件具有很小的保守性。
最后，对本文进行了总结，提出了几个有待研究的问题。
Lur'e system is a class of typical nonlinear system that nonlinear terms are constrained in the finite Hurwitz sector or infinite Hurwitz sector. Almost of all real Lur'e systems may suffer uncertainties in different forms, such as unmodeled dynamics, structured parametric uncertainties, change of the operating environment, model reduction and linearization approximations and external disturbances uncertainties, etc. Usually, these uncertainties are measurable and can be restricted in some range. Robust control theory is an effective way to deal with the control problems with the uncertain systems. On the other hand, quite a number of practical systems with numerous dimensions may have some fast variables taking on singular impulse characteristic, such as electric power system, control system of rolling mill assembly, biochemical process, nuclear reactor, control system of airplane and rocket, and chemical diffused reaction, etc. So, it is important to study the problem of robust control of singular system i
n the domain of control theory. Moreover, large-lag links, transmission process and complicated on-line analyzer etc, are common in the number of industrial processes, which can cause delay in the systems. Such delays will be a main cause of bad performance or even instability for control systems. Therefore, it is found that the problems of robust control for uncertain Lur'e system included time-delays must been fully investigated due to the fact that all above phenomena may occur in the real control systems.
In this paper, the problems of robust control for uncertain Lur'e system with time-delays have been studied. The idea of research rooted in the state system and semistate (singular) system. For state systems and semistate (singular) system, respectively, the problems of robust stability and the design of robust controller have been investigated based on Linear Matrix Inequality (LMI), according to Lyapunov-Razumikhin stability and convex optimization theory, and Barbalat's Lemma and nonsingular linear transformation of model reduction, respectively. The main contents of this paper are outlined as follows,
1 The new absolute stability and stabilization conditions for a class of Lur'e uncertain time-delay systems are proposed through introducing a new state transformation. The result shows that there has been a distinct amelioration in conservation, in comparison with the reported results.
2 The problems of robust stability and robust H# control for a class of Markovian Lur'e jumping system are studied. The sufficient conditions to guarantee robust exponential stability for the closed-loop systems are obtained based on Linear Matrix Inequality, moreover, the approach of design of robust H# output feedback controller is introduced.
3 The problem of reliable H# control for a class of Lur'e systems with polytopic uncertainties is studied when all control components are operational as well as when some control components experience failures, the design approach of reliable H# controller is also obtained.
4 Considering a class of uncertain Lur'e singular system with time-delays, the problem of robust stability is investigated based on Barbalat's Lemma and nonsingular linear transformation of model reduction. Furthermore, the approach of design of robust H# state feedback controller is also introduced.
5 For a class of uncertain Lur'e singular system with time-delays and saturating actuators, the delay-dependent sufficient conditions of robust stability and robust stabilization are addressed, the present results are dependent on the size of delays and don't involve any tuning of parameters, as in the case with the reported results.
6 For unknown statistics characteristics but limited power disturbance, the purpose is concerned with the problem of the robust H# filtering for a class of Lur'e singular system with state time-delays, parameters uncertainties, the sufficient condition is to design a robustly stable filter such that the uncertain Lur'e time-delay singular systems are not only regular
本文研究了不确定Lur’e时滞系统的鲁棒控制问题，研究思路从系统状态的完全性以及状态的不完全性两方面入手。针对完全状态系统，采用LyapunovRazumikhin稳定性理论以及凸优化等重要理论，以线性矩阵不等式作为研究的工具，研究了鲁棒稳定性、鲁棒控制器的设计问题；针对不完全状态(奇异)系统，基于Barbalat引理以及非奇异线性降阶变换，研究了奇异系统的鲁棒稳定性、鲁棒控制器的设计问题。主要研究内容包括如下的几个方面：
1、通过采用一种新的状态变换，提出了一类不确定Lur’e时滞系统时滞依赖的鲁棒稳定及鲁棒二次镇定的新方法，得出的结果与已有的文献相比，保守性有明显地降低。
2、讨论了具有马尔科夫过程的不确定Lur’e跳变系统的鲁棒稳定及鲁棒H_∞控制问题，得到了基于线性矩阵不等式的保证闭环系统鲁棒稳定的充分条件，设计了鲁棒H_∞输出反馈控制器。
3、针对一类具有凸参数不确定性的Lur’e时滞系统，研究了当执行器与传感器分别出现故障的时候的可靠控制问题，得出了可靠H_∞控制器的设计方法。
4、针对一类不确定Lur’e奇异时滞系统，基于Barbalat引理以及非奇异降阶变换，讨论了Lur’e奇异时滞系统的鲁棒稳定问题，提出了鲁棒H_∞状态
浙江大学博士学位论文
反馈控制器的设计方法。
5、针对一类具有饱和执行器的不确定Lur’e奇异系统，提出了时滞依赖的鲁
棒稳定与鲁棒二次镇定的充分条件，所的结果不需要参数的整定。
6、针对任意协方差有界的有色噪声，讨论了一类不确定Lur’e奇异系统的鲁
棒凡滤波问题，得出了鲁棒几滤波器设计的充分条件。
7、针对一类不确定Lur’e时滞系统，通过线性变换，把它转换成奇异系统，
根据奇异系统鲁棒控制理论所得出的鲁棒稳定与鲁棒镇定控制器设计的
充分条件具有很小的保守性。
最后，对本文进行了总结，提出了几个有待研究的问题。
Lur'e system is a class of typical nonlinear system that nonlinear terms are constrained in the finite Hurwitz sector or infinite Hurwitz sector. Almost of all real Lur'e systems may suffer uncertainties in different forms, such as unmodeled dynamics, structured parametric uncertainties, change of the operating environment, model reduction and linearization approximations and external disturbances uncertainties, etc. Usually, these uncertainties are measurable and can be restricted in some range. Robust control theory is an effective way to deal with the control problems with the uncertain systems. On the other hand, quite a number of practical systems with numerous dimensions may have some fast variables taking on singular impulse characteristic, such as electric power system, control system of rolling mill assembly, biochemical process, nuclear reactor, control system of airplane and rocket, and chemical diffused reaction, etc. So, it is important to study the problem of robust control of singular system i
n the domain of control theory. Moreover, large-lag links, transmission process and complicated on-line analyzer etc, are common in the number of industrial processes, which can cause delay in the systems. Such delays will be a main cause of bad performance or even instability for control systems. Therefore, it is found that the problems of robust control for uncertain Lur'e system included time-delays must been fully investigated due to the fact that all above phenomena may occur in the real control systems.
In this paper, the problems of robust control for uncertain Lur'e system with time-delays have been studied. The idea of research rooted in the state system and semistate (singular) system. For state systems and semistate (singular) system, respectively, the problems of robust stability and the design of robust controller have been investigated based on Linear Matrix Inequality (LMI), according to Lyapunov-Razumikhin stability and convex optimization theory, and Barbalat's Lemma and nonsingular linear transformation of model reduction, respectively. The main contents of this paper are outlined as follows,
1 The new absolute stability and stabilization conditions for a class of Lur'e uncertain time-delay systems are proposed through introducing a new state transformation. The result shows that there has been a distinct amelioration in conservation, in comparison with the reported results.
2 The problems of robust stability and robust H# control for a class of Markovian Lur'e jumping system are studied. The sufficient conditions to guarantee robust exponential stability for the closed-loop systems are obtained based on Linear Matrix Inequality, moreover, the approach of design of robust H# output feedback controller is introduced.
3 The problem of reliable H# control for a class of Lur'e systems with polytopic uncertainties is studied when all control components are operational as well as when some control components experience failures, the design approach of reliable H# controller is also obtained.
4 Considering a class of uncertain Lur'e singular system with time-delays, the problem of robust stability is investigated based on Barbalat's Lemma and nonsingular linear transformation of model reduction. Furthermore, the approach of design of robust H# state feedback controller is also introduced.
5 For a class of uncertain Lur'e singular system with time-delays and saturating actuators, the delay-dependent sufficient conditions of robust stability and robust stabilization are addressed, the present results are dependent on the size of delays and don't involve any tuning of parameters, as in the case with the reported results.
6 For unknown statistics characteristics but limited power disturbance, the purpose is concerned with the problem of the robust H# filtering for a class of Lur'e singular system with state time-delays, parameters uncertainties, the sufficient condition is to design a robustly stable filter such that the uncertain Lur'e time-delay singular systems are not only regular
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