Abstract. A new approach to synthesis of modal control of linear system with single input and single output (SISO) is proposed. Stabilization of an unstable object is realized with formalized matrices by means of modification of interval factors of initial matrix in the limited range of their variation. The developed technique allows to carry out displacement of roots of the characteristic equation corresponding to poles of a transfer function, from the right to the left half of complex plane thereby modifying the system dynamics and converting it from the unstable to a steady condition. The difference of matrices corresponding to the new steady and initial unstable system can be identified with the concept of modal control. From the steady formalized matrices received in a piecewise continuous cycle of their factors modification, variety of pointwise and interval matrices of modal control is drawn up.

Keywords: new approach, dynamics of system, stability, displacement of radicals, piecewise continuous cycle, formalized matrices, interval factors, modal control

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