TY - JOUR
T1 - Stability domain of the second‐order discrete oscillatory system with parametric excitation
AU - Tanaka, Toshiyuki
AU - Sato, Chikara
PY - 1989
Y1 - 1989
N2 - This paper presents a quantitative discussion on the stability of the second‐order periodic difference equation, which characterizes the discrete periodic time‐varying system. the periodic parameter discrete system, which corresponds to Mathieu's equation in the continuous system, is represented by a second‐order linear difference equation with a small parameter ε in the varying term. the parameter ε plays an important role in the determination of the stability. By applying McLachlan's method, the expression for the boundary between the stability and the instability can be determined analytically with regard to the parameters contained in the equation. For the case where the periodic parameter of the difference equation is represented as a sum of two even functions, the boundary between stability and instability is determined. the stability can be analyzed in a similar way for the case where the periodic parameter is represented as a sum of N even functions in Fourier series.
AB - This paper presents a quantitative discussion on the stability of the second‐order periodic difference equation, which characterizes the discrete periodic time‐varying system. the periodic parameter discrete system, which corresponds to Mathieu's equation in the continuous system, is represented by a second‐order linear difference equation with a small parameter ε in the varying term. the parameter ε plays an important role in the determination of the stability. By applying McLachlan's method, the expression for the boundary between the stability and the instability can be determined analytically with regard to the parameters contained in the equation. For the case where the periodic parameter of the difference equation is represented as a sum of two even functions, the boundary between stability and instability is determined. the stability can be analyzed in a similar way for the case where the periodic parameter is represented as a sum of N even functions in Fourier series.
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U2 - 10.1002/ecjc.4430720211
DO - 10.1002/ecjc.4430720211
M3 - Article
AN - SCOPUS:0024613097
VL - 72
SP - 109
EP - 116
JO - Electronics and Communications in Japan, Part III: Fundamental Electronic Science (English translation of Denshi Tsushin Gakkai Ronbunshi)
JF - Electronics and Communications in Japan, Part III: Fundamental Electronic Science (English translation of Denshi Tsushin Gakkai Ronbunshi)
SN - 1042-0967
IS - 2
ER -