An improved stability criterion for discrete-time time-delayed Lur’e systemwith sector-bounded nonlinearities

The absolute stability problem of discrete-time time-delayed Lur\u27e systems with sector bounded nonlinearities is investigated in this paper. Firstly, a modified Lyapunov-Krasovskii functional (LKF) is designed with augmenting additional double summation terms, which complements more coupling information between the delay intervals and other system state variables than some previous LKFs. Secondly, some improved delay-dependent absolute stability criteria based on linear matrix inequality form (LMI) are proposed via the modified LKF and the relaxed free-matrix-based summation inequality technique application. The stability criteria are less conservative than some results previously proposed. The reduction of the conservatism mainly relies on the full use of the relaxed summation inequality technique based on the modified LKF. Finally, two common numerical examples are presented to show the effectiveness of the proposed approach

Novel Stabilization Conditions for Uncertain Singular Systems with Time-Varying Delay

The problem of delay-dependent robust stabilization for continuously singular time-varying delay systems with norm-bounded uncertainties is investigated in this paper. First, based on some mathematical transform, the uncertain singular system is described in a form which involves the time-delay integral items. Then, in terms of the delay-range-dependent Lyapunov functional and the LMI technique, the improved delay-dependent LMIs-based conditions are established for the uncertain singular systems with time-varying delay to be regular, causal, and stable. Furthermore, by solving these LMIs, an explicit expression for the desired state feedback control law can be obtained; thus, the regularity, causality, and stability of the closed-loop system are guaranteed. In the end, numerical examples are given to illustrate the effectiveness of the proposed methods

Output feedback robust synchronization of networked Lur'e Systems with incrementally passive nonlinearities

In this paper we deal with robust synchronization problems for uncertain dynamical networks of identical Lur’e systems diffusively interconnected by means of measurement outputs. In contrast to stabilization of one single Lur’e system with a passive static nonlinearity in the negative feedback loop, in the present paper the feedback nonlinearities are assumed to be incrementally passive. We assume that the interconnection topologies among these Lur’e agents are undirected and con- nected throughout this paper. A distributed dynamical protocol is proposed. We establish sufficient conditions for the existence of such protocol that robustly synchronizes the Lur’e dynamical network. The protocol parameter matrices are computed in terms of the system matrices defining the individual agent, but also the second smallest and largest eigenvalues of the Laplacian matrix associated with the interconnection topology

Optimized state feedback regulation of 3DOF helicopter system via extremum seeking

In this paper, an optimized state feedback regulation of a 3 degree of freedom (DOF) helicopter is designed via extremum seeking (ES) technique. Multi-parameter ES is applied to optimize the tracking performance via tuning State Vector Feedback with Integration of the Control Error (SVFBICE). Discrete multivariable version of ES is developed to minimize a cost function that measures the performance of the controller. The cost function is a function of the error between the actual and desired axis positions. The controller parameters are updated online as the optimization takes place. This method significantly decreases the time in obtaining optimal controller parameters. Simulations were conducted for the online optimization under both fixed and varying operating conditions. The results demonstrate the usefulness of using ES for preserving the maximum attainable performance

Flexible structure control laboratory development and technology demonstration

An experimental structure is described which was constructed to demonstrate and validate recent emerging technologies in the active control and identification of large flexible space structures. The configuration consists of a large, 20 foot diameter antenna-like flexible structure in the horizontal plane with a gimballed central hub, a flexible feed-boom assembly hanging from the hub, and 12 flexible ribs radiating outward. Fourteen electrodynamic force actuators mounted to the hub and to the individual ribs provide the means to excite the structure and exert control forces. Thirty permanently mounted sensors, including optical encoders and analog induction devices provide measurements of structural response at widely distributed points. An experimental remote optical sensor provides sixteen additional sensing channels. A computer samples the sensors, computes the control updates and sends commands to the actuators in real time, while simultaneously displaying selected outputs on a graphics terminal and saving them in memory. Several control experiments were conducted thus far and are documented. These include implementation of distributed parameter system control, model reference adaptive control, and static shape control. These experiments have demonstrated the successful implementation of state-of-the-art control approaches using actual hardware

Delay-dependent synchronization criterion for Lur'e systems with delay feedback control

10.1142/S0218127406016677International Journal of Bifurcation and Chaos16103087-309