【摘要】：動(dòng)力系統(tǒng)是一類由連續(xù)時(shí)間系統(tǒng)和離散切換信號(hào)兩部分組成的重要的混雜系統(tǒng),是當(dāng)前研究混雜系統(tǒng)方向最熱門的重要課題.脈沖系統(tǒng)作為混雜系統(tǒng)重要組成部分,在許多方面都有相當(dāng)廣泛的應(yīng)用.另外一種重要的組成部分為切換系統(tǒng),該系統(tǒng)是由一系列的子系統(tǒng)和邏輯規(guī)則來協(xié)調(diào)各個(gè)切換.為了更好地研究這類混雜系統(tǒng),我們把它們結(jié)合為一種新的系統(tǒng),即:脈沖切換系統(tǒng).輸入-狀態(tài)穩(wěn)定性由Sontag首次提出,在脈沖切換系統(tǒng)領(lǐng)域很有研究?jī)r(jià)值,并且推廣到非線性系統(tǒng).輸入-狀態(tài)穩(wěn)定性意味著無論初始狀態(tài)是多少,如果輸入信號(hào)足夠小,狀態(tài)最終會(huì)無限小.在本文的研究中,我們引入不穩(wěn)定子系統(tǒng),運(yùn)用多重Lyapunov方法,得出脈沖切換系統(tǒng)的輸入-狀態(tài)穩(wěn)定性和隨機(jī)輸入-狀態(tài)穩(wěn)定性.本文的主要結(jié)論可以概括為以下兩個(gè)部分:1)脈沖切換非線性系統(tǒng)的輸入-狀態(tài)穩(wěn)定性.在多重Lyapunov函數(shù)方法和平均脈沖區(qū)間條件下,我們對(duì)輸入到狀態(tài)穩(wěn)定性的研究分三種情況討論,即:所有子系統(tǒng)穩(wěn)定,所有子系統(tǒng)不穩(wěn)定和部分子系統(tǒng)不穩(wěn)定.如果所有子系統(tǒng)穩(wěn)定,即使脈沖影響為不穩(wěn)定脈沖,在有下界的脈沖切換區(qū)間條件下,系統(tǒng)仍然為輸入-狀態(tài)穩(wěn)定.進(jìn)一步地,如果所有子系統(tǒng)不穩(wěn)定,在有上界的平均脈沖區(qū)間和穩(wěn)定脈沖影響下,系統(tǒng)仍然為輸入-狀態(tài)穩(wěn)定.然而,如果存在部分子系統(tǒng)穩(wěn)定部分子系統(tǒng)不穩(wěn)定,在特定的條件下,仍然可以證明系統(tǒng)為輸入-狀態(tài)穩(wěn)定.最后,仿真例子證明了結(jié)果的正確性.2)隨機(jī)脈沖切換非線性系統(tǒng)的隨機(jī)輸入-狀態(tài)穩(wěn)定性.研究了一類脈沖切換非線性系統(tǒng),考慮隨機(jī)輸入-狀態(tài)穩(wěn)定性問題.基于Lyapunov函數(shù)方法,給出了保證系統(tǒng)隨機(jī)輸入-狀態(tài)穩(wěn)定性的充要條件.然后,借助平均脈沖區(qū)間技巧,也分三種情況進(jìn)行討論.在脈沖影響的作用下,仍然可以證明系統(tǒng)的隨機(jī)輸入-狀態(tài)穩(wěn)定性.最后,仿真例子證明了結(jié)果的正確性.
[Abstract]:Dynamical system is an important hybrid system which consists of continuous time system and discrete switched signal. As an important part of hybrid system, impulse system is widely used in many fields. Another important component is the handoff system, which is coordinated by a series of subsystems and logic rules. In order to study this kind of hybrid systems better, we combine them into a new system, that is, impulsive switched systems. Input-state stability is proposed by Sontag for the first time. It has great research value in the field of impulsive switched systems and is extended to nonlinear systems. Input-state stability means that no matter what the initial state is, if the input signal is small enough, the state will eventually be infinitely small. In this paper, we introduce the unstable subsystem and obtain the input-state stability and stochastic input-state stability of impulsive switched systems by using the multiplex Lyapunov method. The main conclusions of this paper can be summarized as follows: 1) Input-state stability of impulsive switched nonlinear systems. Under the condition of multiple Lyapunov functions and average impulsive intervals, we discuss the stability of input states in three cases: stability of all subsystems, instability of all subsystems and instability of some subsystems. If all subsystems are stable, even if the pulse effect is unstable, the system is still input-state stable under the condition of lower bound pulse switching interval. Furthermore, if all subsystems are unstable, the system is still input-state stable under the influence of the average pulse interval with upper bound and the stable pulse. However, if some subsystems are stable and some subsystems are unstable, it can still be proved that the system is input-state stable under certain conditions. Finally, a simulation example is given to show the correctness of the results. 2) Stochastic input-state stability of stochastic impulsive switched nonlinear systems. In this paper, a class of impulsive switched nonlinear systems is studied. The problem of stochastic input-state stability is considered. Based on the Lyapunov function method, a necessary and sufficient condition is given to guarantee the stochastic input-state stability of the system. Then, with the help of the average pulse interval technique, it is also discussed in three cases. The stochastic input-state stability of the system can still be proved under the influence of impulses. Finally, a simulation example is given to show the correctness of the results.
【學(xué)位授予單位】：曲阜師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O19

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相關(guān)期刊論文 前1條

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本文編號(hào)：2377378