This paper deals with the problem of finite-time boundedness and fin计e-time stabilization boundedness of frax?tional-order switched nonlinear systems with exogenous inputs.By constructing a simple Lyapunov-like funct...This paper deals with the problem of finite-time boundedness and fin计e-time stabilization boundedness of frax?tional-order switched nonlinear systems with exogenous inputs.By constructing a simple Lyapunov-like function and using some properties of Caputo derivative,the authors obtain some new sufficient conditions for the problem via linear matrix inequalities,which can be efficiently solved by using existing convex algorithms.A constructive geometric is used to design switching laws amongst the subsystems.The obtained results are more general and useful than some existing works,and cover them as special cases,in which only linear fractional-order systems were presented.Numerical examples are provided to demonstrate the effectiveness of the proposed results.展开更多
This paper is concerned with the problem of guaranteed cost finite-time control of fractionalorder nonlinear positive switched systems (FONPSS) with D-perturbation. Firstly, the proof of the positivity of FONPSS with ...This paper is concerned with the problem of guaranteed cost finite-time control of fractionalorder nonlinear positive switched systems (FONPSS) with D-perturbation. Firstly, the proof of the positivity of FONPSS with D-perturbation is given, the definition of guaranteed cost finite-time stability is firstly given in such systems. Then, by constructing linear copositive Lyapunov functions and using the mode-dependent average dwell time (MDADT) approach, a static output feedback controller is constructed, and sufficient conditions are derived to guarantee that the corresponding closed-loop system is guaranteed cost finite-time stable (GCFTS). Such conditions can be easily solved by linear programming. Finally, an example is provided to illustrate the effectiveness of the proposed method.展开更多
针对线性时不变高阶MIMO系统模型难以直接进行计算分析的问题,对高阶模型进行模型降阶。依据模型降阶理论,对线性时不变系统进行Lyapunov方程求解,得到线性系统的完全可控Gramians矩阵和完全可观Gramians矩阵,对Gramians矩阵进行Cholesk...针对线性时不变高阶MIMO系统模型难以直接进行计算分析的问题,对高阶模型进行模型降阶。依据模型降阶理论,对线性时不变系统进行Lyapunov方程求解,得到线性系统的完全可控Gramians矩阵和完全可观Gramians矩阵,对Gramians矩阵进行Cholesky分解,得到Cholesky分解因子,分解因子通过SVD(singular value decomposition)法求得Hankel奇异值,从而确定系统的平衡变换阵。计算可控可观Gramians矩阵的左右特征空间基底矩阵,利用左右特征空间的基底矩阵求得原系统降阶的系统,通过Hankel SVD方法确定降阶之后的误差范围。利用Matlab对SLICOT测试库中的便携式CDPlayer 120阶的高阶模型进行降阶,获取到50、30、20阶的降阶模型,对研究算法进行验证,结果表明,降阶效果理想。展开更多
基金supported by the National Natural Science Foundation of China(61573332,61601431)Fundamental Research Funds for the Central Universities(WK2100100028)
基金funded by the Ministry of Education and Training of Vietnam under Grant No.TN-487,led by Assoc.Prof.Phan Thanh Nam,Quy Nhon University,Decision number 5650/QDBGDDT 28/12/2018
文摘This paper deals with the problem of finite-time boundedness and fin计e-time stabilization boundedness of frax?tional-order switched nonlinear systems with exogenous inputs.By constructing a simple Lyapunov-like function and using some properties of Caputo derivative,the authors obtain some new sufficient conditions for the problem via linear matrix inequalities,which can be efficiently solved by using existing convex algorithms.A constructive geometric is used to design switching laws amongst the subsystems.The obtained results are more general and useful than some existing works,and cover them as special cases,in which only linear fractional-order systems were presented.Numerical examples are provided to demonstrate the effectiveness of the proposed results.
基金supported by the National Natural Science Foundation of China under Grant Nos.U1404610,61473115 and 61374077Fundamental Research Project under Grant Nos.142300410293,142102210564 in the Science and Technology Department of Henan Province+1 种基金the Science and Technology Research Key Project under Grant No.14A413001 in the Education Department of Henan ProvinceYoung Key Teachers Plan of Henan Province under Grant No.2016GGJS-056
文摘This paper is concerned with the problem of guaranteed cost finite-time control of fractionalorder nonlinear positive switched systems (FONPSS) with D-perturbation. Firstly, the proof of the positivity of FONPSS with D-perturbation is given, the definition of guaranteed cost finite-time stability is firstly given in such systems. Then, by constructing linear copositive Lyapunov functions and using the mode-dependent average dwell time (MDADT) approach, a static output feedback controller is constructed, and sufficient conditions are derived to guarantee that the corresponding closed-loop system is guaranteed cost finite-time stable (GCFTS). Such conditions can be easily solved by linear programming. Finally, an example is provided to illustrate the effectiveness of the proposed method.
文摘针对线性时不变高阶MIMO系统模型难以直接进行计算分析的问题,对高阶模型进行模型降阶。依据模型降阶理论,对线性时不变系统进行Lyapunov方程求解,得到线性系统的完全可控Gramians矩阵和完全可观Gramians矩阵,对Gramians矩阵进行Cholesky分解,得到Cholesky分解因子,分解因子通过SVD(singular value decomposition)法求得Hankel奇异值,从而确定系统的平衡变换阵。计算可控可观Gramians矩阵的左右特征空间基底矩阵,利用左右特征空间的基底矩阵求得原系统降阶的系统,通过Hankel SVD方法确定降阶之后的误差范围。利用Matlab对SLICOT测试库中的便携式CDPlayer 120阶的高阶模型进行降阶,获取到50、30、20阶的降阶模型,对研究算法进行验证,结果表明,降阶效果理想。
