【摘要】 采用Chebyshev多项式展开法,将线性周期时变系统的解转化成一系列的代数方程的解,并近似求得系统的单值矩阵。结合Floquet理论,通过分析该矩阵的特征值可判断相应解的稳定性。数值计算结果表明了该法的可行性。更多还原

【Abstract】 For a linear system with periodic parameters, the state vector and the periodic matrix of the system is expanded in terms of Chebyshev polynomials over the principal period at first. Such an expansion reduces the original problem to a set of linear algebraic equations from which the solution in the interval of one period can be obtained. Then, the transition matrix at the end of one period with Flouquet theory is obtained, which can provide the stability conditions via an eigen-analysis procedure. Furthermore, numerical results show this method is available.更多还原