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This paper addresses the problem of exponential stability and stabilization for a class of delayed distributed parameter systems, which is modeled by partial integro-differential equations (PIDEs). By employing the vector-valued Wirtinger's inequality, the sufficient condition of exponential stability of the PIDE system with a given decay rate is investigated. The condition is presented by linear matrix inequality (LMIs). After that, we develop a spatial proportional-integral-derivative state-feedback controller that ensures the exponential stabilization of the PIDE system in terms of LMIs. Finally, numerical examples are presented to verify the effectiveness of the proposed theoretical results. [ABSTRACT FROM AUTHOR]

This paper concerns the global stabilization of an underactuated spring-coupled three-link horizontal manipulator (STHM), which is an underactuated mechanical system (UMS) with two actuators and three degrees of freedom (DOF). A new control method is developed that asymptotically stabilizes the STHM at the origin using the position measurements of the manipulator only. First, we introduce a homeomorphic coordinate transformation for the STHM system. This changes the stabilization of the STHM into that of the transformed system. Next, we analyze the characteristics of the transformed system. After that, we construct an equivalent-input-disturbance- (EID-) based control system to globally stabilize the transformed system at the origin. Finally, a numerical example demonstrates the validity of the presented method. Our method only uses the position measurements of the STHM to design stabilizing controller. It reduces the cost of the whole control system and avoids the influence on the system’s control performance imposed by velocity noises. In addition, the analysis and control method of this paper is easy to extend to the global stabilization of other n -DOF ( n ⩾ 3 ) UMSs. [ABSTRACT FROM AUTHOR]

This paper studies the existence and stability of periodic solution of the high-order discrete-time Cohen–Grossberg neural networks with varying delays. The properties of M-matrix and the contracting mapping principle are used to obtain a sufficient condition that guarantees the uniqueness and global exponential stability of the periodic solution. In addition, a numerical example is given that demonstrates the effectiveness of the proposed theoretical results. [ABSTRACT FROM AUTHOR]

Abstract: This paper concerns the existence and exponential stability of periodic solution for the high-order discrete-time bidirectional associative memory (BAM) neural networks with time-varying delays. First, we present the criteria for the existence of periodic solution based on the continuation theorem of coincidence degree theory and the Young’s inequality, and then we give the criteria for the global exponential stability of periodic solution by using a non-Lyapunov method. After that, we give a numerical example that demonstrates the effectiveness of the theoretical results. The criteria presented in this paper are easy to verify. In addition, the proposed analysis method is easy to extend to other high-order neural networks. [Copyright &y& Elsevier]