【摘要】：在控制理論的研究中,時(shí)滯系統(tǒng)備受關(guān)注。時(shí)滯存在于自然界的各種系統(tǒng)之中,它嚴(yán)重影響系統(tǒng)的動(dòng)態(tài)性能。如果需要構(gòu)建更加精確的模型,就不能忽略時(shí)滯對系統(tǒng)性能的影響,所以研究時(shí)滯系統(tǒng)具有重要的理論價(jià)值和實(shí)際意義。但是,目前很難找到一種普遍適用的方法解決此類問題,所以需要采用不同的方法研究各類時(shí)滯系統(tǒng)。本文基于前人的工作,對線性區(qū)間時(shí)變時(shí)滯系統(tǒng)和非線性Luire時(shí)變時(shí)滯系統(tǒng)進(jìn)行深入研究。構(gòu)造包含更多信息的Lyapunov泛函,采用減少放大程度的界定方法都可以有效優(yōu)化結(jié)果�？紤]線性區(qū)間時(shí)變時(shí)滯系統(tǒng),在構(gòu)造Lyapunov泛函時(shí),盡可能包含更多的時(shí)滯信息,并通過Jensen不等式結(jié)合倒數(shù)凸組合方法和Jensen不等式結(jié)合自由權(quán)矩陣方法界定泛函導(dǎo)數(shù)積分項(xiàng),得到時(shí)滯依賴穩(wěn)定性判據(jù)�？紤]非線性Lurie時(shí)變時(shí)滯系統(tǒng),在構(gòu)造Lyapunov泛函時(shí),盡可能包含更多的系統(tǒng)信息,通過Wirtinger不等式結(jié)合倒數(shù)凸組合方法界定泛函導(dǎo)數(shù)積分項(xiàng),并應(yīng)用S-procedure過程處理泛函導(dǎo)數(shù),得到時(shí)滯依賴穩(wěn)定性判據(jù)。通過MATLAB仿真求解線性矩陣不等式,從而得到使系統(tǒng)漸近穩(wěn)定的Lyapunov泛函�；谙到y(tǒng)的穩(wěn)定性判據(jù),給出系統(tǒng)滿足H_∞性能的充分條件,并設(shè)計(jì)系統(tǒng)的狀態(tài)反饋控制器。通過MATLAB仿真求得系統(tǒng)的反饋增益矩陣并搭建Simulink模型。最后通過數(shù)值算例驗(yàn)證結(jié)果的正確性。
[Abstract]:In the study of control theory, time-delay systems have attracted much attention. Time delay exists in various systems in nature, which seriously affects the dynamic performance of the system. If a more accurate model is needed, the influence of time delay on system performance can not be ignored, so it is of great theoretical and practical significance to study time-delay systems. However, it is difficult to find a universal and applicable method to solve this kind of problem, so it is necessary to use different methods to study all kinds of time-delay systems. In this paper, based on the previous work, linear interval time-varying time-delay systems and nonlinear Luire time-varying time-delay systems are deeply studied. The Lyapunov functional with more information can be constructed, and the results can be effectively optimized by using the definition method to reduce the magnification. In this paper, linear interval time-varying time-delay systems are considered. When constructing Lyapunov Functionals, more delay information is included as much as possible, and the functional derivative integral terms are defined by Jensen inequality combined with reciprocal convex combination method and Jensen inequality combined with free matrix method. The delay dependent stability criterion is obtained. In this paper, nonlinear Lurie time-varying time-delay systems are considered. When constructing Lyapunov Functionals, more system information is included as much as possible. The functional derivative integral term is defined by Wirtinger inequality combined with reciprocal convex combination method, and the functional derivatives are dealt with by S-procedure process. The delay dependent stability criterion is obtained. The linear matrix inequality (LMI) is solved by MATLAB simulation, and the Lyapunov functional which makes the system asymptotically stable is obtained. Based on the stability criterion of the system, the sufficient conditions for the system to satisfy the H _ 鈭，

本文編號(hào)：2484570