This paper presents the applications of the stability-equation method to the analysis and design of linear systems. Control systems with multiple inputs and outputs are considered; the absolute stability and relative stability characteristics are analyzed. Stability conditions for control systems with a transport lag or a distributive lag are presented. Finally, the stability characteristics of a system with a distributive parameter are analyzed. Notation Ag2) AR(2) 0(8) C*(8) F*(8) H I I,~ Kp K~ M o e ~8 ~(s) R, R*(8) S T~ 3 ~ (F, 8) 2 2R, 2Ri 2,, 2H imaginary stability equation real stability equation output vector complex output matrix transfer function complex transfer function angular momentum of spin rotor momentum of inertia of spin rotor imaginary part H/I product of the coefficients of the highest terms of AR(2) and Al(2) controller of gyro control system input vector real part complex input Laplace operator settling time root distribution of F(S) = 0 in the S-plane operator (2 = -is) root of real stability equation root of imaginary stability equation rotation angle of imaginary axis Y. T. Tsay and K. lV. Han as shifting quantity of imaginary axis damping ratio a real part of S ยขo imaginary part of S