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Applications of the general root-locus theory for nonlinear systems

The general root locus theory is a theory of designing, analysis and synthesis of root hodographs in arbitrary variation laws of any preset parameters of automatic control systems and their combinations. On this basis it is considered an analysis of absolute stability, hyperstability, L-stability of nonlinear control systems. A root hodograph of conical sections is used, under which we name the mapping of curve of the second order of complex plane W=G(p), W-u+iv onto a complex plane p-+i, realized by means of a function inverse to the function of the linear part of the system. Root conditions require that for a system to be absolutely stable it is necessary that all the branches of at least one root hodograph of conical images are located completely on the left semiplane of plane p.