Design of controller for a class of pendulum-like system guaranteeing dichotomy

In this paper the problems of controller design for a class of nonlinear pendulum-like control system with multiple equilibria guaranteeing dichotomy and gradient-like property of the closed-loop systems are investigated. By applying KYP-lemma and some results of positive real control the method of controller design based on linear matrix inequality is proposed.     

Robust analysis and synthesis for a class of uncertain nonlinear systems with multiple equilibria

This paper focuses on a class of uncertain nonlinear systems which are subject to norm-bounded parameter uncertainty in the forward path and a vector-valued periodic nonlinearity in the feedback path, and addresses robust analysis and synthesis problems for such systems. Sufficient conditions for global asymptotic stability are derived in terms of linear matrix inequalities (LMIs) and a technique for the estimation of the uncertainty bound is proposed by solving a generalized eigenvalue minimization problem. The problem of robust synthesis is concerned with designing a feedback controller such that the resulting closed-loop system is globally asymptotically stable for all admissible uncertainties. It is shown that a solution to the robust synthesis problem for the uncertain system can be obtained by solving a synthesis problem for an uncertainty free system. A concrete example is presented to demonstrate the applicability and validity of the proposed approach.     

Robust stabilization for a class of nonlinear networked control systems

The problem of robust stabilization for a class of uncertain networked control systems （NCSs） with nonlinearities satisfying a given sector condition is investigated in this paper. By introducing a new model of NCSs with parameter uncertainty, network-induced delay, nonlinearity and data packet dropout in the transmission, a strict linear matrix inequality （LMI） criterion is proposed for robust stabilization of the uncertain nonlinear NCSs based on the Lyapunov stability theory. The maximum allowable transfer interval （MATI） can be derived by solving the feasibility problem of the corresponding LMI. Some numerical examples are provided to demonstrate the applicability of the proposed algorithm.     

Control of a class of pendulum-like systems with Lagrange stability

In this paper, the control problem of linear perturbed systems is investigated. Some strategies of controller design guaranteeing the closed-loop systems with property of pendulum-like and Lagrange stability are proposed. The given method is applied to the system of synchronous single-phase motor with pulsing vibrating moment.     

Non-fragile observer-based robust control for a class of fractional-order nonlinear systems

The paper is concerned with the problem of the observer-based robust control for a class of fractional-order nonlinear systems. First, by introducing a continuous frequency distributed equivalent model and using indirect Lyapunov approach, the sufficient condition for robust asymptotic stability of the closed-loop system via state observer-based control is presented, which is less conservative than some existing ones in recent literature. Next, using matrix’s singular value decomposition (SVD) and linear matrix inequality (LMI) techniques, the existence condition and method of designing a robust non-fragile observer-based controller are derived. Finally, the validity of the proposed methods are demonstrated by two numerical examples.     

Delay-dependent robust stabilization for a class of neutral systems with nonlinear perturbations

This note deals with the problem of stabilization/stability for neutral systems with nonlinear perturbations. A new stabilization/stability scheme is presented. Using improved Lyapunov functionals, less conservative stabilization/stability conditions are derived for such systems based on linear matrix inequalities (LMI). Numerical examples are provided to show that the proposed results significantly improve the allowed upper bounds of the delay size over some existing ones in the literature.     

一类非线性系统的函数观测器设计

研究单边Lipschitz非线性系统的函数观测器设计.基于线性矩阵不等式获得了函数观测器增益矩阵存在的条件,然后提出函数观测器增益矩阵的设计方法.通过一个仿真实例,验证所设计的函数观测器不仅能够估计系统的状态,而且可使观测误差快速收敛到零.     

A new delay-dependent absolute stability criterion for a class of nonlinear neutral systems

This paper deals with absolute stability for a class of nonlinear neutral systems using a discretized Lyapunov functional approach. A delay-dependent absolute stability criterion is obtained and formulated in the form of linear matrix inequalities (LMIs). The criterion is valid not only for systems with small delay, but also for systems with non-small delay. Neither model transformation nor bounding technique for cross terms, nor free weighting matrix method is involved through derivation of the stability criterion. Numerical examples show that for small delay case, the results obtained in this paper significantly improve the estimate of the stability limit over some existing result in the literature; for non-small delay case, the ideal results can also be achieved.     

Delay-dependent observer-based stabilizing controller design for linear multiple state-delayed systems

This article concerns a coupled LMIs approach to delay-dependent observer-based output feedback stabilizing controller design for linear continuous-time systems with multiple state delays. The advantage of our proposed delay-dependent coupled LMIs criterion lies in that: (1) it can optimize one of multiple time delays with others selected properly, and at the same time, the feedback-gain and observer-gain can be obtained, respectively. (2) it is less conservative than the existing delay-independent ones in the literature. Algorithm to solve the coupled LMIs is also given. Numerical examples illustrate the effectiveness of our method.     

Reliable guaranteed cost sampling control for nonlinear time-delay systems

The problem of reliable guaranteed cost sampling control is investigated for nonlinear time-delay systems in this paper. Sufficient conditions for the existence of state feedback controller are derived in terms of linear matrix inequities (LMIs), which guarantee asymptotic stability with the provided performance index for the normal and possible actuator faults cases. The related optimization problem is also offered to minimize the guaranteed cost performance bound. Illustrative examples are given to show the validity of the present control scheme.     

Delay-dependent robust stabilization for a class of neutral systems with nonlinear perturbations

This note deals with the problem of stabilization/stability for neutral systems with nonlinear perturbations. A new stabilization/stability scheme is presented. Using improved Lyapunov functionals, less conservative stabilization/stability conditions are derived for such systems based on linear matrix inequalities （LMI）. Numerical examples are provided to show that the proposed results significantly improve the allowed upper bounds of the delay size over some existing ones in the literature.     

Robust guaranteed cost control for uncertain stochastic systems with multiple decision makers

The guaranteed cost control (GCC) problem for uncertain stochastic systems with N decision makers is investigated. It is noteworthy that the necessary conditions, which are determined from Karush-Kuhn-Tucker (KKT) conditions, for the existence of a guaranteed cost controller have been derived on the basis of the solutions of cross-coupled stochastic algebraic Riccati equations (CSAREs). It is shown that if CSAREs have an optimal solution, then the closed-loop system is exponentially mean square stable (EMSS) and has a cost bound. In order to simplify computations and attain a global optimum, the linear matrix inequality (LMI) technique is also considered. Finally, a numerical example for a practical megawatt-frequency control problem shows that the proposed methods can help in attaining an adequate cost bound. Furthermore, the features of these methods are characterized.     

New synthesis algorithm of static output feedback sliding mode control for a class of uncertain systems

Based on a kind of regular form,a Lyapunov matrix with special structure is presented to design the sliding surface matrix conveniently and then an effective algorithm is developed on it. A simple static output feedback sliding mode control law without extra dynamic equation is given, such that the predefined shding surface is reached in finite time for the general matching uncertainties. In the reported result, this extra dynamic equation is used for evaluating the norm bound of the unmeasured state vector. Finally, some examples are studied to illustrate the proposed approach.     

一类时变时滞系统的稳定性分析

针对时变时滞系统稳定性问题, 在考虑非线性扰动的情况下, 为了降低时变时滞系统稳定性判据的保守性, 以改进的Jensen 不等式, Wirtinger型双重积分不等式以及优化凸组合技术为基础, 构造增广的Lyapunov-Krasovskii 泛函, 得到了新的时滞相关稳定性判据. 最后, 通过数值仿真对比可知, 该稳定性判据具有较小的保守性和良好的鲁棒性.     

Robust adaptive neural observer design for a class of nonlinear parabolic PDE systems

A robust adaptive neural observer design is proposed for a class of parabolic partial differential equation (PDE) systems with unknown nonlinearities and bounded disturbances. The modal decomposition technique is initially applied to the PDE system to formulate it as an infinite-dimensional singular perturbation model of ordinary differential equations (ODEs). By singular perturbations, an approximate nonlinear ODE system that captures the dominant (slow) dynamics of the PDE system is thus derived. A neural modal observer is subsequently constructed on the basis of the slow system for its state estimation. A linear matrix inequality (LMI) approach to the design of robust adaptive neural modal observers is developed such that the state estimation error of the slow system is uniformly ultimately bounded (UUB) with an ultimate bound. Furthermore, using the existing LMI optimization technique, a suboptimal robust adaptive neural modal observer can be obtained in the sense of minimizing an upper bound of the peak gains in the ultimate bound. In addition, using two-time-scale property of the singularly perturbed model, it is shown that the resulting state estimation error of the actual PDE system is UUB. Finally, the proposed method is applied to the estimation of temperature profile for a catalytic rod.     

一类3--D非线性系统的稳定性分析及函数观测器设计

本文首先研究了一类3--D非线性系统的稳定性问题,在此基础上,利用秩条件和线性矩阵不等式(LMI)方法,得到了这类系统的渐近函数观测器存在的充分条件,并给出了函数观测器的设计方法.最后,通过算例来说明这种方法是可行且有效的.     

一类结构不确定采样系统的鲁棒控制

针对一类结构不确定性线性采样系统，在时域中用Lyapunov方法研究采样系统的鲁棒控制及最优鲁棒控制，给出了系统鲁棒稳定的充分条件以及相应的鲁棒控制律，控制律的求取借助于求解一类线性矩阵不等式（LMI），或求解满足特定线性不等式条件下的优化问题，算例结果表明，采样周期是一个关键性的设计参数。     

一类具有区间时变多状态时滞系统的稳定性分析

研究一类具有区间时变多状态时滞且时滞导数不确定的系统的稳定性问题. 通过选择合理的Lyapunov-Krasovskii函数结合辅助变量和广义状态法, 以LMI的形式给出了时滞相关的稳定性充分条件. 文中的结论对时滞的导数没有任何限制, 可用于具有快时变时滞系统. 与已有的相关研究成果相比, 结论更具有一般性, 保守性也更低. 最后通过仿真及数值算例说明了本文方法的有效性和优越性.     

Integrated observer based fault estimation for a class of Lipschitz nonlinear systems

The fault estimation for a class of nonlinear systems with Lipschitzian nonlinearities and faults is studied in this article. An integrated estimation observer that covers the robust estimation observer (REO) and adaptive estimation observer (AEO) is proposed to improve the accuracy of fault estimation. Compared with the traditional AEO, the designed observer does not involve the output derivatives and can be more suitable for practical applications. Furthermore, based on the designed observer, the coupling term emerging in the obtained error dynamics can be eliminated reasonably and less conservative stability conditions for the error dynamics can be obtained, whereas the case is hard to be achieved based on the existing intermediate estimator approach in the literature. Compared with the traditional REO and AEO, the fault can be estimated with a good accuracy by using the proposed integrated estimation observer. Numerical examples test the effectiveness and advantages of the proposed method.     

Improved delay-dependent stability criteria for systems with a delay varying in a range

This paper provides improved delay-dependent stability criteria for systems with a delay varying in a range. The criteria improve over some previous ones in that they have fewer matrix variables yet less conservatism, which is established theoretically. An example is given to show the advantages of the proposed results.