Stability of a class of coupled systems

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

“…The dynamical system (1) arises naturally in a wide range of applications, including: teleoperator systems, mechanical multi-body systems and robotics control (see for instance [20,[27][28][29][30] [22][23][24]). Now, the synchronization error of the master and slave systems (1) and (2) (1) and (2), namely synchronization error system, can be expressed by …”

“…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.…”

Mixed H2/H∞ output-feedback control of second-order neutral systems with time-varying state and input delays

“…In mechanical systems pairs of the matrices (M, M 1 ), (A, A 1 ) and (B, B 1 ) correspond to the mass, damping, and stiffness matrices and x(t) is the vector of generalized displacements. The matrices F and F 1 distribute the force input to the correct degrees of freedom (see [34][35][36]). …”

“…It is noted that the second-order neutral system (1) is controlled by a proportional and derivative (PD) mixed H 2 /H ∞ output-feedback control which has a direct application in the control of artificial satellites using motor driven inertia wheels as a source of torque (see for instance [36]). When rank(M) < n, both the open-loop system (1) and the closedloop system (1) by (3) are singular ones.…”

“…Second-order systems capture the dynamic behavior of many natural phenomena, and have found applications in many fields, such as vibrational and structural analysis, spacecraft control, electrical networks, robotics control and, hence, have attracted much attention (see, for instance, [34][35][36][37][38][39][40][41][42][43]). In the literature, a Haar-wavelet-based method for finite-time H 2 control problem of the second-order retarded linear systems with respect to a quadratic cost function for any length of time is proposed in [44].…”