Optimization algorithms for stabilization of multi-input vibration system with time delay using eigenvalues assignment technique

The study considers the robust and minimum norm problems for stabilization using partial eigenvalue assignment technique in nonsingular vibration system with time delay via the acceleration-velocity-displacement active controller. The new gains expressions of active controller are derived by orthogonality relations, which keeps the no spill-over property of the vibration system. To discuss the stabilization problem using eigenvalues assignment technique, the linear equation is solved by constructing a special matrix which is proved to be nonsingular. Solving algorithm is proposed to obtain the parametric expressions of active controller. A new gradient-based optimization method is proposed to discuss the robust and minimum norm controller design by establishing the gradient formulas of cost functions. The optimization algorithm is proposed to discuss the robust and minimum norm stabilization of closed-loop eigenvalues in vibration system with time delay. The presented algorithms are feasible to the case of time delay between measurements of state and actuation of control. Numerical examples show the effectiveness of the method.