Abstract
Although state-space representation has provided advanced and mathematical analysis in modern control theory, existence of non-autonomous input vector prevents a simple expression of vector-matrix product in state equation. It is because non-autonomous external force cannot be expressed as a function of merely a state vector. In this study, we decompose an arbitral non-autonomous intermittent function of an external force for a 1DOF oscillator into vibration manipulation functions, which represent internal forces in a closed Hamilton system of three vibro-impact oscillators designed for Grover algorithm. Through the sequential decompositions and their unsmooth joints, each piecewise input vector is taken into a new state-space representation of a simple product of an extended state vector with state matrices of Grover operators. From this point of view, we could regard the intermittent change of the state vector with piecewise input as a manipulation of coherent phonons under the control of quantum algorithm in the intermittently closed Hamiltonian system with discrete impulsive interactions from environment. This might suggest an answer of an inverse problem in Newtonian mechanics, which pursuits isolated systems from dynamics with non-autonomous force.
