不确定时滞系统的鲁棒稳定性分析

【作者】 吴寒寒；

【导师】 孔淑兰；

【作者基本信息】 曲阜师范大学 ， 应用数学， 2010， 硕士

【摘要】 不确定时滞系统的鲁棒稳定性分析是目前自动控制领域研究的一个热点.由于系统环境的变化、元器件的老化以及某些物理参数随时间的未知变化等因素所带来的系统行为的改变都会导致系统模型不确定性和时滞的产生.不确定性和时滞的存在使得系统的分析与综合变得更加复杂和困难,同时也是系统不稳定和系统性能变差的根源.本文从理论分析的角度,考虑不确定性、时滞、线性、非线性、干扰和自适应跟踪等动态特性,利用二次稳定性、Lyapunov稳定性以及线性矩阵不等式等重要理论与方法,分别研究了系统的状态反馈二次稳定控制器、在H∞范数界γ约束下稳定性控制器、鲁棒H∞保性能控制器、自适应输出反馈控制器以及系统的自适应跟踪控制器的综合问题,提出了相对统一的处理框架.研究结果表明,在一定的条件下,各类系统稳定化控制器的综合问题均可以转化为相应的Riccati方程(不等式)或线性矩阵不等式的可行性解问题,而Riccati方程(不等式)或线性矩阵不等式的求解已有成熟的算法,从而使研究结果具有可操作性,为进一步研究不确定时滞系统的鲁棒控制问题奠定了基础.更多还原

【Abstract】 At present the robust stability analysis of systems with uncertain time-delay is focused on automatic control field. Many factors, such as changing of systems environment, the age of components, and some physical param-eters and so on, can bring about changes of the systems behaviors. Those will cause uncertainty and time-delay of the system models. The existence of uncertainty and time-delay makes the system analysis and synthesis become more complex and more difficult. At the same time, it is also the source of the systems instability and systems performance deterioration. Uncer-tainty, time-delay, linear, nonlinear, disturbances and adaptive tracking are considered from the perspective of theoretical analysis. Quadratic stabiliza-tion, Lyapunov stabilization, linear matrix inequalities and other important theories and methods are used in this paper. The paper studys the synthe-sis problems of the systems state feedback quadratic stabilization controller, stability controller constrained under the H∞bounded normγ, robust H∞guaranteed cost controller, adaptive output feedback controller and adaptive tracking controller, respectively. A relatively unified processing framework is proposed. The results show that the integrated problems of various systems stabilizing controller can be transformed into the feasibility of solutions of the corresponding Riccati equations (inequalities) or linear matrix inequali-ties under the certain conditions, however, the solution of Riccati equations (inequalities) and linear matrix inequalities have the sophisticated algorithms. So the research results are operable which establish the foundation for further study robust control problem of uncertain time-delay systems.更多还原