本文選題：分?jǐn)?shù)階系統(tǒng) + 奇異系統(tǒng)��； 參考：《河北師范大學(xué)》2016年博士論文

【摘要】：分?jǐn)?shù)階系統(tǒng)是由微分階次為任意實數(shù)甚至復(fù)數(shù)的微分方程所描述的動力學(xué)系統(tǒng).分?jǐn)?shù)階控制系統(tǒng)是指被控系統(tǒng)為分?jǐn)?shù)階系統(tǒng)或者控制器為分?jǐn)?shù)階控制器的控制系統(tǒng).本文以分?jǐn)?shù)階系統(tǒng)作為研究對象,主要從分?jǐn)?shù)階奇異系統(tǒng)、分?jǐn)?shù)階模糊系統(tǒng)、同分?jǐn)?shù)階非線性系統(tǒng)以及多分?jǐn)?shù)階非線性系統(tǒng)的穩(wěn)定性與反饋控制等四個方面進(jìn)行了研究.本文的主要研究內(nèi)容包括:(1)研究了一類分?jǐn)?shù)階奇異不確定系統(tǒng)的穩(wěn)定性與反饋控制問題.首先,根據(jù)分?jǐn)?shù)階奇異系統(tǒng)的穩(wěn)定性理論,針對分?jǐn)?shù)階屬于01的分?jǐn)?shù)階奇異不確定系統(tǒng),給出了判斷該類系統(tǒng)魯棒漸近穩(wěn)定的充分條件.其次,通過矩陣的奇異值分解和線性矩陣不等式(LMI)技術(shù),討論了分?jǐn)?shù)階奇異不確定系統(tǒng)的反饋控制問題,并設(shè)計了合適的狀態(tài)反饋和輸出反饋控制器,使得閉環(huán)系統(tǒng)是漸近穩(wěn)定的.最后,通過三個數(shù)值仿真實例均驗證了所得結(jié)論的正確性與設(shè)計思想的有效性.(2)研究了兩類分?jǐn)?shù)階T-S模糊不確定系統(tǒng)的穩(wěn)定性與反饋控制問題.首先,利用分?jǐn)?shù)階線性系統(tǒng)的穩(wěn)定性理論,針對分?jǐn)?shù)階屬于01以及1≤2兩種不同情況下,分別給出了判斷這兩類分?jǐn)?shù)階T-S模糊不確定系統(tǒng)魯棒漸近穩(wěn)定的充分條件.其次,通過LMI技術(shù),討論了分?jǐn)?shù)階T-S模糊不確定系統(tǒng)的模糊反饋控制問題,并設(shè)計了合適的模糊輸出反饋控制器,使得閉環(huán)系統(tǒng)對于所有可容許的不確定項是漸近穩(wěn)定的.最后,通過兩個數(shù)值仿真實例分別驗證了所得結(jié)論的正確性與設(shè)計思想的有效性.(3)研究了一類同分?jǐn)?shù)階非線性不確定系統(tǒng)的穩(wěn)定性與反饋控制問題.首先,根據(jù)分?jǐn)?shù)階系統(tǒng)Lyapunov穩(wěn)定性理論,針對分?jǐn)?shù)階屬于01的同分?jǐn)?shù)階非線性不確定系統(tǒng),給出了判斷該類系統(tǒng)魯棒漸近穩(wěn)定的充分條件.其次,通過LMI技術(shù),討論了同分?jǐn)?shù)階非線性不確定系統(tǒng)的反饋控制問題,并設(shè)計了合適的狀態(tài)反饋控制器,使得閉環(huán)系統(tǒng)是漸近穩(wěn)定的.最后,通過對同分?jǐn)?shù)階混沌Liu系統(tǒng)進(jìn)行數(shù)值仿真驗證了所得結(jié)論的正確性與設(shè)計思想的有效性.(4)研究了一類多分?jǐn)?shù)階非線性系統(tǒng)反饋控制問題.首先,利用多分?jǐn)?shù)階非線性系統(tǒng)的穩(wěn)定性理論,給出了分?jǐn)?shù)階屬于01的多分?jǐn)?shù)階非線性受控系統(tǒng)在不同平衡點處漸近穩(wěn)定的充分條件.其次,利用受控系統(tǒng)在平衡點處Jacobian矩陣的特征值,設(shè)計了合適的狀態(tài)反饋控制器,使得閉環(huán)系統(tǒng)在不同平衡點處是漸近穩(wěn)定的.最后,通過對多分?jǐn)?shù)階的非混沌捕食-食餌系統(tǒng)和混沌Chen系統(tǒng)進(jìn)行數(shù)值仿真分別驗證了所得結(jié)論的正確性與設(shè)計思想的有效性.
[Abstract]:Fractional order system is a dynamic system described by differential equations with differential order being arbitrary real number or even complex number. Fractional control system refers to the control system which is a fractional system or a controller is a fractional controller. In this paper, fractional order systems are studied in four aspects: fractional singular systems, fractional fuzzy systems, nonlinear systems of the same fractional order and the stability and feedback control of multi-fractional nonlinear systems. In this paper, we study the stability and feedback control of a class of fractional singular uncertain systems. Firstly, according to the stability theory of fractional singular systems, a sufficient condition is given to judge the robust asymptotic stability of fractional singular uncertain systems with fractional order 01. Secondly, the feedback control problem of fractional singular uncertain systems is discussed by using singular value decomposition of matrices and LMI technique, and appropriate state feedback and output feedback controllers are designed. The closed loop system is asymptotically stable. Finally, three numerical simulation examples are given to verify the correctness of the conclusions and the validity of the design idea.) the stability and feedback control problems of two classes of fractional T-S fuzzy uncertain systems are studied. Firstly, by using the stability theory of fractional linear systems, sufficient conditions for judging the robust asymptotic stability of these two classes of fractional T-S fuzzy uncertain systems are given for the two different cases of fractional order 0 1 and 1 鈮，

本文編號：1877518