Reliable $$H_{\infty }$$ Stabilization of Fuzzy Systems with Random Delay Via Nonlinear Retarded Control

In this paper, the robust reliable \(H_\infty \) control problem has been investigated for a class of nonlinear discrete-time TS fuzzy systems with random delay. In particular, the proposed fuzzy system consists of local nonlinear models with set of fuzzy rules, but the conventional TS fuzzy systems has local linear models. Our attention is focused on the design of a feedback reliable nonlinear retarded control law to ensure the robust asymptotic stability for nonlinear discrete-time TS fuzzy system with admissible uncertainties as well as actuator failure cases and random delay. In particular, by using an input delay approach, the random delay with stochastic parameters in the system matrices is introduced in the system model. Based on the Lyapunov approach, firstly, a sufficient condition for asymptotic stability is proposed for TS fuzzy systems in the presence of actuator failures. Then, a robust reliable \(H_\infty \) control is designed for the uncertain TS fuzzy system by solving a strict linear matrix inequalities using the available numerical software. Finally, a numerical example based on real-time ball and beam system is provided to validate the effectiveness of the proposed design technique.     

Robust Stability and $$H_{\infty }$$ Control of Discrete-Time Uncertain Impulsive Systems with Time-Varying Delay

This paper considers the robust stability and \(H_{\infty }\) control problems for a class of discrete-time uncertain impulsive systems with time-varying delay. Sufficient conditions for the robust stability, stabilization and \(H_\infty \) control of the considered systems are developed. Some numerical examples are presented to show the effectiveness of the theoretical results.     

$$H_\infty $$ Model Reduction for the Distillation Column Linear System

In the paper, the problem of model reduction is considered for the distillation column linear system. For a given stable distillation column linear system, the objective is to find the construction of a reduced-order model, which approximates the original system well in the robust \(H_\infty \) performance. Some sufficient conditions to characterize the \(H_\infty \) norm bound error performance are proposed in terms of linear matrix inequalities (LMIs). Following the proposed projection approach, the \(H_\infty \) model reduction problem is solved, which casts the model reduction subject to LMIs constraints. Finally, a practical example of the distillation column linear system is provided to illustrate the effectiveness of the proposed method.     

Robust state feedback $$H_\infty $$ control for uncertain 2-D continuous state delayed systems in the Roesser model

This paper is concerned with the problem of robust state feedback \(H_\infty \) stabilization for a class of uncertain two-dimensional (2-D) continuous state delayed systems. The parameter uncertainties are assumed to be norm-bounded. Firstly, a new delay-dependent sufficient condition for the robust asymptotical stability of uncertain 2-D continuous systems with state delay is developed. Secondly, a sufficient condition for \(H_\infty \) disturbance attenuation performance of the given system is derived. Thirdly, a stabilizing state feedback controller is proposed such that the resulting closed-loop system is robustly asymptotically stable and achieves a prescribed \(H_\infty \) disturbance attenuation level. All results are developed in terms of linear matrix inequalities. Finally, two examples are provided to validate the effectiveness of the proposed method.     

Finite frequency $$H_\infty $$ control of 2-D continuous systems in Roesser model

This paper investigates the finite frequency (FF) \(H_\infty \) control problem of two-dimensional (2-D) continuous systems in Roesser Model. Our attention is focused on designing state feedback controllers guaranteeing the bounded-input-bounded-output stability and FF \(H_\infty \) performance of the corresponding closed-loop system. A generalized 2-D Kalman-Yakubovich-Popov (KYP) lemma is presented for 2-D continuous systems. By the generalized 2-D KYP lemma, the existence conditions of \(H_\infty \) controllers are obtained in terms of linear matrix inequalities. Two examples are given to validate the proposed methods.     

Analysis and Design of $$H_{\infty }$$ Controllers for 2D Singular Systems with Delays

The \(H_{\infty }\) control design problem is solved for the class of 2D discrete singular systems with delays. More precisely, the problem addressed is the design of state-feedback controllers such that the acceptability, internal stability and causality of the resulting closed-loop system are guaranteed, while a prescribed \(H_\infty \) performance level is simultaneously fulfilled. By establishing a novel version of the bounded real lemma, a linear matrix inequality condition is derived for the existence of these \(H_\infty \) controllers. They can then be designed by solving an iterative algorithm based on LMI optimizations. An illustrative example shows the applicability of the algorithm proposed.     

$$H_{\infty }$$ Performance Analysis of 2D Continuous Time-Varying Delay Systems

This paper deals with the problem of \(H_{\infty }\) performance analysis of 2D continuous time-varying delay systems described by Roesser model. Using a simple Lyapunov–Krasovskii functional, a new delay-dependent stability criterion is derived in terms of linear matrix inequalities. The obtained result is then extended to the problem of \(H_{\infty }\) performance analysis. Several examples are provided in order to illustrate the effectiveness of our results.     

Quantized Feedback Adaptive Reliable $$H_{\infty }$$ Control for Linear Time-Varying Delayed Systems

Based on an improved \(H_\infty \) performance index, the method of designing a reliable adaptive \(H_\infty \) controller with quantized state is addressed for the time-varying delayed system in this paper. On the basis of online estimates of actuator faults, the controller parameters are updated automatically to compensate the influence of actuator faults on the system while the desired improved \(H_\infty \) performance is preserved. A Lyapunov function candidate is constructed to prove that the closed-loop system is asymptotically stable. And the existing sufficient conditions of the controller are proved to be less conservative. The gains of the controller and the parameters of the adaptive law are co-designed and obtained in terms of solutions to a set of linear matrix inequalities. Finally, two numerical examples are given to illustrate that the proposed method is more effective than the previous methods for time-varying delayed systems.     

基于观测器的含扰动Lipschitz非线性系统鲁棒控制

针对一类含扰动Lipschitz非线性系统的鲁棒控制问题进行了研究,讨论了基于观测器的非线性系统鲁棒控制问题.首先,对满足Lipschitz条件的非线性系统构造出了状态观测器;其次,考虑到系统中的扰动项,根据Lyapunov理论分两种情况以线性矩阵不等式的形式给出基于状态观测器的控制器存在的充分条件,得到了观测器增益矩...     

Robust Delay-Dependent Stability Criteria for Dynamic Systems with Nonlinear Perturbations and Leakage Delay

This paper studies the global asymptotic stability for uncertain systems with mixed delays. The mixed delays include constant delay in the leakage term (i.e., leakage delay) and time-varying delays. The uncertainties under consideration are nonlinear time-varying parameter perturbations and norm-bounded uncertainties. Based on a appropriate Lyapunov–Krasovskii functional with triple integral terms, some integral inequalities and convex combination technique, a novel delay-dependent stability criterion is derived in terms of linear matrix inequalities (LMIs). Finally, three numerical examples are included to show the superiority of the proposed method.     

A novel word length selection method for a guaranteed $$H_\infty $$ interference rejection performance and overflow oscillation-free realization of 2-D digital filters

This paper examines the problem of the local overflow stability and disturbance attenuation performance analysis of two-dimensional (2-D) Roesser digital filters in the presence of external interferences. In particular, by utilizing the local properties of saturation nonlinearity and Lyapunov stability theory, a novel linear matrix inequality (LMI)-based condition is proposed that not only ensures the nonexistence of overflow oscillations, but also yields the \(H_{\infty }\) interference rejection performance of 2-D digital filters under the overflow constraint. It is worth mentioning here that in contrast to the traditional approaches based on modeling the saturation with a global sector-bound condition, the proposed approach provides a less conservative bound for the attenuation of disturbances and renders the idea of minimum word length for realizing the 2-D (Roesser) filter to eliminate overflow oscillations and attain the specified \(H_{\infty }\) interference attenuation performance index. Finally, a numerical simulation example is also provided, which demonstrates the superiority of the proposed method over the existing techniques.     

多时滞Cohen-Grossberg神经网络鲁棒稳定性的新判据

分析了一类具有多时滞及参数摄动的Cohen-Grossberg神经网络的全局鲁棒稳定性.通过构造适当的Lyapunov泛函,以线性矩阵不等式形式给出了平衡点全局鲁棒稳定的判据.此外,所有结论的建立都不需要假定互连矩阵的对称性及激活函数的可微性和单调性.仿真结果进一步证明了结论的有效性.     

Stability and $${L_{\infty }}$$-Gain Analysis for Positive Switched Systems with Time-Varying Delay Under State-Dependent Switching

This paper investigates the problems of stability and \({L_\infty }\)-gain analysis for a class of positive switched systems with time-varying delay. Attention is focused on designing a state-dependent switching rule such that the system satisfies a prescribed \({L_\infty }\)-gain performance level, where the proposed scheme does not require the switching instants to be known in advance. By constructing an appropriate co-positive type Lyapunov–Krasovskii functional, sufficient conditions for exponential stability with \({L_\infty }\)-gain performance of the underlying systems are derived. Furthermore, the stability along the switching surface is analyzed. Finally, two examples are presented to demonstrate the effectiveness of the proposed method.     

A Study of a Robust Fuzzy Controller for Perturbed Nonlinear Systems

In this paper, a fuzzy logic controller (FLC) for a nonlinear system with uncertain perturbation is proposed. Based on the Lyapunov synthesis approach, we construct the FLC not only to stabilize the perturbed nonlinear system but also to guarantee a prescribed H_∞ norm bound of the closed-loop transfer function from the disturbance to the controlled output. A given example illustrates the availability of the proposed design method.     

New Stability Condition of T-S Fuzzy Systems and Design of Robust Flight Control Principle

Unlike the previous research works analyzing the stability of the T-S (Takagi-Sugeno) fuzzy model, an extension on the stability condition of T-S fuzzy systems with a different strategy is provided. In the strategy a new variable, which is relative to the grade of fuzzy membership function, is introduced to the stability analysis and a new stability conclusion is deduced. The definition of stability condition in this paper is different from previous works, though they are similar in form. With the proposed method, the simulation in flight control law shows a better effectiveness.     

New Stability Condition of T-S Fuzzy Systems and Design of Robust Flight Control Principle

Unlike the previous research works analyzing the stability of the T-S (Takagi?Sugeno) fuzzy model, an extension on the stability condition of T-S fuzzy systems with a different strategy is provided. In the strategy a new variable, which is relative to the grade of fuzzy membership function, is introduced to the stability analysis and a new stability conclusion is deduced. The definition of stability condition in this paper is different from previous works, though they are similar in form. With the proposed method, the simulation in flight control law shows a better effectiveness.