Robust Eigenstructure Assignment in Quadratic Matrix Polynomials: Nonsingular Case

An optimization approach for minimum norm and robust partial quadratic eigenvalue assignment problems for vibrating structures

“…Suppose that a control force of the form Bu(t), (see Refs. [3,25]) is applied to the structure. Here B is a given real n × m matrix (m ≤ n) and u(t) is a real m-vector given by…”

LMI-based H ∞ synchronization of second-order neutral master-slave systems using delayed output feedback control

“…The methods for synchronization of the chaotic systems have been widely studied in recent years, and many different methods have been applied theoretically and experimentally to synchronize chaotic systems, such as feedback control [4][5][6][7][8][9][10], adaptive control [11][12][13][14][15], backstepping [16] and sliding mode control [17][18][19][20][21]. One of the most attractive dynamical systems is the second-order systems which capture the dynamic behaviour of many natural phenomena, and have found applications in many fields, such as vibration and structural analysis, spacecraft control, electrical networks, robotics control and, hence, have attracted much attention (see, for instance, [22][23][24][25][26][27][28][29][30][31][32]). It has been proved that in special situations a second-order system may show chaotic dynamics.…”

Solutions of the Partially Described Inverse Quadratic Eigenvalue Problem

“…Furthermore, in some other recent articles, Chu/Datta [1,5], Nichol and Kautsky [9] as well as Datta/Elhay/Ram/Sarkissian [6,10] considered a feedback design for a second-order control system that leads to a partial eigenstructure assignment problem for the QEP. The proportional and derivative feedback controllers can assign specific eigenpairs and make the resulting system insensitive to perturbations, but can not keep the new QEP symmetric.…”