摘要
现实中的许多过程都可以用广义系统来建模,例如,受限控制系统,电路系统,某些人口增长模型以及奇异扰动系统等。由于广义系统比正常系统可以更好地描述物理现象,所以广义系统的稳定性和控制问题受到了极大关注。和正常系统相比,广义系统有更复杂的结构。考虑到时滞和不确定性对广义系统的影响,时滞不确定广义系统的鲁棒稳定性和控制问题已有许多研究结果。然而,大部分的结果都是在基于控制器是可以被精确执行的假设下提出的。在控制器不能被精确执行时,就需要设计不确定广义系统的非脆弱控制器,这就是本文研究的主要问题。具体如下:
第三章研究了一类时滞不确定广义系统的非脆弱保性能控制器设计问题,所考虑的不确定性是范数有界的,且系统状态和控制输入都存在时变时滞,设计出带有反馈增益扰动的控制器能够保证闭环系统是正则,无脉冲,指数稳定的,且性能函数存在上界。
第四章研究了一类时变时滞不确定广义系统的非脆弱H∞控制问题。在系统矩阵,滞后状态矩阵,输入矩阵和滞后输入矩阵都具有不确定性时,设计出带有反馈增益扰动的控制器能够保证闭环系统是正则,无脉冲,α?稳定的,且满足H_∞性能条件γ。
在第五章中,给出了线性广义系统的有限时间有界的概念,然后对有外界扰动的不确定广义系统,设计一类非脆弱控制器,使得闭环系统是无脉冲且是有限时间有界。
Many practical processes can be modeled as descriptor systems, such as constrained control problems, electrical circuits, certain population growth models and singular perturbations. In the past several decades, stability and control problems of descriptor systems have been extensively studied due to the fact that the descriptor system better describes physical systems than the state-space systems. Compared with state-space systems, the descriptor system has a more complicated yet richer structure. Considering the effect of time delay and uncertainty on the dynamical performance of the systems, robust stability and control problems have been more recently investigated for the uncertain descriptor systems with time delay. However, most results are under the assumption that the designed controller can be exactly implemented. When the controller can’t be exactly implemented, we should design non-fragile controller for uncertain descriptor systems, this is the main content of this paper, specifically as follows:
In chapter 3, we consider the design problem of non-fragile guaranteed cost controller for uncertain descriptor systems with time delays. The considered uncertainties are norm-bounded and the time delays are time-varying and exist both in the state and control input. The designed controller with inaccuracies exist in control gain can guarantee the closed-loop system is regular, impulse-free, exponentially stable and there is an upper bound of the cost function.
In chapter 4, the problem of non-fragile H-infinity control for uncertain descriptor systems with time-varying delays is addressed. The controller is designed when parameter uncertainties exist in system matrix, delayed system state matrix, control input matrix, delayed control input matrix, and inaccuracies exist in control gain, so as to guarantee that the closed-loop system is regular, impulse-free,α?stable ,also satisfies a prescribed H-infinity performance condition.
In chapter 5, we generalize the concepts of finite time bounded to linear singular systems. Then, non-fragile finite time control problem is considered for linear singular systems with parametric uncertainties and exogenous disturbance,the controller can guarantee that the closed-loop system is impulse-free and finite time bounded.
引文
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