Non-Fragile Controller Design for 2-D Discrete Uncertain Systems Described by the Roesser Model

This paper is concerned with the design problem of non-fragile controller for a class of two-dimensional (2-D) discrete uncertain systems described by the Roesser model. The parametric uncertainties are assumed to be norm-bounded. The aim of this paper is to design a memoryless non-fragile state feedback control law such that the closed-loop system is asymptotically stable for all admissible parameter uncertainties and controller gain variations. A new linear matrix inequality (LMI) based sufficient condition for the existence of such controllers is established. Finally, a numerical example is provided to illustrate the applicability of the proposed method.

Robust Non-Fragile Control of 2-D Discrete Uncertain Systems: An LMI Approach

This paper considers the problem of robust non-fragile control for a class of two-dimensional (2-D) discrete uncertain systems described by the Fornasini-Marchesini second local state-space (FMSLSS) model under controller gain variations. The parameter uncertainty is assumed to be norm-bounded. The problem to be addressed is the design of non-fragile robust controllers via state feedback such that the resulting closed-loop system is asymptotically stable for all admissible parameter uncertainties and controller gain variations. A sufficient condition for the existence of such controllers is derived based on the linear matrix inequality (LMI) approach combined with the Lyapunov method. Finally, a numerical example is illustrated to show the contribution of the main result.

Robust Suboptimal Guaranteed Cost Control for 2-D Discrete Systems Described by Fornasini-Marchesini First Model

This paper considers the guaranteed cost control problem for a class of two-dimensional (2-D) uncertain discrete systems described by the Fornasini-Marchesini (FM) first model with norm-bounded uncertainties. New linear matrix inequality (LMI) based characterizations are presented for the existence of static-state feedback guaranteed cost controller which guarantees not only the asymptotic stability of closed loop systems, but also an adequate performance bound over all the admissible parameter uncertainties. Moreover, a convex optimization problem is formulated to select the suboptimal guaranteed cost controller which minimizes the upper bound of the closed-loop cost function.

LMI Approach to Suboptimal Guaranteed Cost Control for 2-D Discrete Uncertain Systems

This paper studies the problem of the guaranteed cost control via static-state feedback controllers for a class of two-dimensional (2-D) discrete systems described by the Fornasini-Marchesini second local state-space (FMSLSS) model with norm bounded uncertainties. A convex optimization problem with linear matrix inequality (LMI) constraints is formulated to design the suboptimal guaranteed cost controller which ensures the quadratic stability of the closed-loop system and minimizes the associated closed-loop cost function. Application of the proposed controller design method is illustrated with the help of one example.

Delay-Dependent Robust H∞ Control for Uncertain 2-D Discrete State Delay Systems Described by the General Model

This paper considers the problem of delay-dependent robust optimal H∞ control for a class of uncertain two-dimensional (2-D) discrete state delay systems described by the general model (GM). The parameter uncertainties are assumed to be norm-bounded. A linear matrix inequality (LMI)-based sufficient condition for the existence of delay-dependent g-suboptimal state feedback robust H∞ controllers which guarantees not only the asymptotic stability of the closed-loop system, but also the H∞ noise attenuation g over all admissible parameter uncertainties is established. Furthermore, a convex optimization problem is formulated to design a delay-dependent state feedback robust optimal H∞ controller which minimizes the H∞ noise attenuation g of the closed-loop system. Finally, an illustrative example is provided to demonstrate the effectiveness of the proposed method.

Robust Optimal H∞ Control for Uncertain 2-D Discrete State-Delayed Systems Described by the General Model

This paper investigates the problem of robust optimal H∞ control for uncertain two-dimensional (2-D) discrete state-delayed systems described by the general model (GM) with norm-bounded uncertainties. A sufficient condition for the existence of g-suboptimal robust H∞ state feedback controllers is established, based on linear matrix inequality (LMI) approach. Moreover, a convex optimization problem is developed to design a robust optimal state feedback controller which minimizes the H∞ noise attenuation level of the resulting closed-loop system. Finally, two illustrative examples are given to demonstrate the effectiveness of the proposed method.

Ergodic Rate Analysis on Applying Antenna Selection in D2D Communication Underlaying Cellular Networks

By reusing the spectrum of a cellular network, device-to-device(D2D) communications is known to greatly improve the spectral efficiency bypassing the base station(BS) of the cellular network. Antenna selection is the most cost efficient scheme for interference management, which is crucial to D2D systems. This paper investigates the achievable rate performance of the D2D communication underlaying the cellular network where a multiple-antenna base station with antenna selection scheme is deployed. We derive an exact closed-form expression of the ergodic achievable rate. Also, using Jensen's inequality, two pairs of upper and lower bounds of the rate are derived and we validate the tightness of the two sets of bounds. Based on the bounds obtained, we analyze the ergodic achievable rate in noise-limited scenario, interference-limited high SNR scenario and larger-scale antenna systems. Our analysis shows that the presence of D2D users could be counter-productive if the SNR at cellular UE is high. Further analysis shows that the relationship between the ergodic rate and the number of antennas it positive, but keeps decreasing as the antenna number increasing. These show the inefficiency of antenna selection in D2D interference management.

基于Jensen不等式的2-D区间时变时滞系统的稳定与控制

考虑具有区间时变时滞二维(2-D)离散系统的时滞相关稳定性和控制问题.选取含有时滞上下界的Lyapunov函数,对其差分时考虑到所有项,结合2-DJensen不等式,由线性矩阵不等式给出系统新的时滞相关稳定性准则.准则中含有更少的待定变量,降低了数值计算负担,并且比一些已有结果具有更小的保守性.基于稳定性准则,由状态反馈实现了系统的稳定控制.最后,通过数值算例表明了所得结果的有效性和优越性.

Robust state feedback for uncertain 2-D discrete switched systems in the Roesser model

The design of robust H_(∞)controllers is considered here for a class of two-dimensional(2-D)discrete switched systems described by the Roesser model with polytopic uncertainties.Attention focuses on the design of a switched state feedback controller,which guarantees the robust asymptotic stability and a prescribedH_(∞)performance for the closed-loop system.By using multiple parameter-dependent Lyapunov functionals,and introducing some switched free-weighting matrices,a new sufficient condition for the robust H_(∞)performance analysis of uncertain 2-D discrete switched systems is developed.Furthermore,the design of switched state feedback controller is proposed in terms of linear matrix inequalities(LMIs).Illustrative examples are given to illustrate the effectiveness of the developed theoretical results.