【摘要】：時(shí)滯現(xiàn)象大量存在于網(wǎng)絡(luò)控制系統(tǒng)、機(jī)械傳動(dòng)系統(tǒng)以及經(jīng)濟(jì)系統(tǒng)等各類系統(tǒng)中。時(shí)滯往往導(dǎo)致動(dòng)態(tài)性能不良,甚至不穩(wěn)定,同時(shí)在某些控制系統(tǒng)中時(shí)滯又可以改善控制效果。因此對(duì)時(shí)滯系統(tǒng)的穩(wěn)定性研究在系統(tǒng)與控制領(lǐng)域中有重要的理論意義和現(xiàn)實(shí)價(jià)值,近年來(lái)得到了國(guó)內(nèi)外學(xué)者的廣泛關(guān)注。首先,本文總結(jié)了目前研究時(shí)滯穩(wěn)定性的主要方法,重點(diǎn)對(duì)積分不等式方法進(jìn)行了深入的研究,進(jìn)而針對(duì)連續(xù)時(shí)滯系統(tǒng)提出了一種新的研究時(shí)滯相關(guān)穩(wěn)定性的積分不等式方法——推廣的二重積分不等式方法。針對(duì)離散時(shí)滯系統(tǒng),提出了新的基于Abel型有限和不等式的離散不等式方法。這兩個(gè)不等式將包含更多時(shí)滯信息項(xiàng)。特別地,許多文獻(xiàn)比較了積分不等式的方法和自由權(quán)矩陣的方法,盡管兩種方法在對(duì)導(dǎo)數(shù)項(xiàng)的估計(jì)和放大程度的效果上幾乎相當(dāng),但積分不等式的方法表達(dá)形式簡(jiǎn)潔,減少很多決策變量,減輕了計(jì)算負(fù)擔(dān),因而積分不等式方法展現(xiàn)出了其優(yōu)越性。其次,應(yīng)用新的不等式,并結(jié)合Lyapunov泛函方法,分別針對(duì)分布時(shí)滯系統(tǒng),中立型時(shí)滯系統(tǒng),廣義時(shí)滯系統(tǒng)和離散時(shí)滯系統(tǒng)這四種情況,研究了時(shí)滯系統(tǒng)的時(shí)滯相關(guān)穩(wěn)定性,得到了基于線性矩陣不等式(LMIs)的一系列時(shí)滯相關(guān)穩(wěn)定性判據(jù),所得結(jié)果從理論和數(shù)值例子上加以說(shuō)明該方法具有較小的保守性。最后,對(duì)全文所做的工作進(jìn)行了總結(jié),并指出了下一步研究的方向。
[Abstract]:The phenomenon of time delay exists in many kinds of systems, such as network control system, mechanical transmission system, economic system and so on. Time delay often leads to poor dynamic performance and even instability. At the same time, time delay can improve the control effect in some control systems. Therefore, the study of the stability of time-delay systems has important theoretical significance and practical value in the field of system and control, and has been widely concerned by scholars at home and abroad in recent years. Firstly, this paper summarizes the main methods to study the stability of time delay, with emphasis on the integral inequality method, and then proposes a new integral inequality method for continuous time delay systems, which is the extended double integral inequality method, which studies the delay dependent stability. A new discrete inequality method based on Abel type finite sum inequality is proposed for discrete time-delay systems. These two inequalities will contain more information terms with time delay. In particular, many literatures compare the method of integral inequality with the method of free matrix. Although the two methods have almost the same effect on the estimation and amplification of derivative terms, the method of integral inequality is simple in expression, reduces many decision variables and lightens the burden of calculation, so the method of integral inequality shows its advantages. Secondly, by using the new inequality and Lyapunov functional method, the delay-dependent stability of time-delay systems is studied for distributed time-delay systems, neutral time-delay systems, generalized time-delay systems and discrete time-delay systems, respectively. A series of delay-dependent stability criteria based on linear matrix inequality (LMIs) are obtained. The results show that the method is less conservative in theory and numerical examples. Finally, the work done in this paper is summarized, and the direction of the next research is pointed out.
【學(xué)位授予單位】：青島大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O231

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本文編號(hào)：2506499