The article presents a new method for determining the clustering conditions of the roots of the characteristic equation of a closed-loop control system in a given region of the complex plane. This method allows obtaining the required indicators of the quality of transient processes of the system - the oscillation of the system and the degree of its stability [1]. The method is used to place the roots of the system in a special truncated angular region of the left half-plane, the boundaries of which are determined by the specified values of these quality indicators. The derivation of universal analytical expressions applicable to systems of arbitrary order is given, which significantly expands the scope of practical application of the method. In this paper, we consider two formulations of the problem. The first formulation is oriented toward systems with fixed boundary angles of the sector domain, which corresponds to many typical technical requirements. The second, more general formulation provides for the possibility of arbitrarily specifying the slope angles of the domain boundaries with subsequent approximation and the introduction of restrictions on the real parts of the roots. The developed algorithm allows not only to analyze existing systems, but also to synthesize new ones, forming the corresponding characteristic polynomial and calculating the necessary restrictions on its coefficients. The efficiency and relative simplicity of the method implementation makes it a promising tool for engineering calculations when designing automatic control systems for various purposes.