Stability analysis of discrete-time systems with actuator saturation by a saturation-dependent Lyapunov function

In this paper, stability of discrete-time linear systems subject to actuator saturation is analyzed using a saturation-dependent Lyapunov function. This saturation-dependent Lyapunov function captures the real-time information on the severity of actuator saturation and leads to less conservative estimate of the domain of attraction, which is based on the solution of an LMI optimization problem. Numerical examples are presented to show the effectiveness of the proposed method.     

Stability analysis and controller synthesis for discrete linear time-delay systems with state saturation nonlinearities

The problem of global asymptotic stability analysis and controller synthesis for a class of discrete linear time-delay systems with state saturation nonlinearities is investigated. With the introduction of a free matrix whose infinity norm is less than or equal to 1, the state of discrete linear time-delay systems with state saturation is bounded by a convex hull, which makes it feasible to apply a suitable Lyapunov functional to obtain a sufficient condition for global asymptotic stability. It is also shown that this condition can be extended to controller synthesis and discrete time-delay systems with partial state saturation. The obtained results are expressed in terms of matrix inequalities that can be solved by the presented iterative linear matrix inequality approach. The effectiveness of these results is demonstrated by some numerical examples.     

状态饱和线性离散系统的H∞ 控制

研究一类具有状态饱和约束的离散线性系统的 ∞控制问题.通过引入一个无穷范数小于等于1的自由变量,将状态饱和约束下的离散线性系统状态变量约束在一个凸多面体内.在此基础上,给出了状态饱和离散线性系统的有界实引理,并研究了状态反馈控制律设计算法.所给出的结论表示为双线性矩阵不等式,可通过所提出的迭代线性矩阵不等式算法求解.最后通过数值例子验证了所提出算法的正确性和有效性.     

状态饱和离散线性系统的稳定性分析

讨论一类具有状态饱和非线性的离散线性系统稳定性分析问题. 通过引入无穷范数小于等于1 的自由矩阵与对角元素非正的对角矩阵, 将状态饱和离散线性系统的状态变量约束在一个凸多面体内, 进而以矩阵不等式形式给出状态饱和离散线性系统的稳定性判据, 并给出该矩阵不等式的迭代线性矩阵不等式算法. 基于这一稳定性判据, 给出了基于迭代线性矩阵不等式的状态反馈控制律设计算法. 通过状态饱和离散线性系统的状态空间分割方法, 给 出了保守性更小的稳定性判据, 并给出了相应的迭代线性矩阵不等式算法. 数值例子验证了所给出方法的正确性与有效性.

     

Analysis and design for singular discrete linear systems subject to actuator saturation

A method to estimate the domain of attraction for a singular discrete linear system under a saturated linear feedback is established. Simple conditions are derived in terms of an auxiliary feedback matrix for determining if a given ellipsoid is contractively invariant. These conditions are expressed in terms of linear matrix inequalities. The largest contractively invariant ellipsoid can also be determined by solving an optimization problem with linear matrix inequality constraints. This result is extended to the design of feedback gain that results in the largest contractively invariant ellipsoid, which is also a linear matrix inequality optimization problem. A numerical example demonstrates the applicability and effectiveness of the presented method. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Stability analysis for delta operator systems subject to state saturation

In this paper, we investigate the problem of stability analysis for linear delta operator systems subject to state saturation. Both full state saturation and partial state saturation are investigated for the delta operator systems. Two equivalent necessary and sufficient conditions are identified such that the system with full state saturation is globally asymptotically stable. Based on the sufficient conditions, an iterative algorithm is proposed for testing global asymptotic stability of the system with full state saturation. A new globally asymptotically stable condition is also proposed for the partial state saturation system. Two numerical examples on a ball and beam model are given to show the effectiveness of the proposed method.     

A new stability analysis and controller design method for discrete-time linear systems with saturation nonlinearities

The problems of stability analysis and controllers design for discrete-time linear systems subject to state saturation nonlinearities are investigated in this paper. Both full state saturation and partial state saturation are considered. It is well known to all that the controller design problem under state saturation is very difficult and complex to deal with. In order to overcome the difficulty, a new and tractable system is constructed, and it can be proved that the constructed system is with the same domain of attraction as the original system. With the aid of this property, to estimate the domain of attraction of the original system, an LMI-based method is presented for estimating the domain of attraction of the origin for the new constructed system under state saturation. Further, two optimization algorithms are developed for constructing dynamic output-feedback controllers and state feedback controllers, respectively, which guarantee that the domain of attraction of the origin for the closed-loop system is as ’large’ as possible. An example is provided to demonstrate the effectiveness of the new method.     

H_∞ controller synthesis of piecewise discrete time linear systems

This paper presents an H∞ controller design method for pieccwise discrete time linear systems based on a piecewise quadratic Lyapunov function. It is shown that the resulting closed loop system is globally stable with guaranteed H∞ perfomiance and the controller can be obtained by solving a set of bilinear lnatrLx inequalities. It has been shown that piecewise quadratic Lyapunov functions are less conservative than the global qnadnmc Lyapunov functions. A simulation example is also given to illustrate the advantage of the proposed approach.     

Stability analysis for continuous-time systems with actuator saturation

The aim of this paper is to study the determination of the stability regions for continuous-time systems subject to actuator saturation. Using an affine saturation-dependent Lyapunov function, a new method is proposed to obtain the estimation of the domain of attraction of the closed-loop system. A family of linear matrix inequalities （LMIs） that provides sufficient conditions for the existence of this type of Lyapunov function are presented. The results obtained in this paper can reduce the conservativeness compared with the existing ones. Numerical examples are given to illustrate the effectiveness of the proposed results.     

H∞ control for linear systems with state saturation nonlinearities

The problem of H_∞ control for a class of linear systems with state saturation nonlinearities is considered in this paper. By introducing a row diagonally dominant matrix with negative diagonal elements and a diagonal matrix with positive elements, the H_∞ control problem is reduced to a matrix inequality feasibility problem that can be solved by the proposed iterative linear matrix inequality algorithm. The effectiveness of the presented method is demonstrated by a numerical example. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

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.     

Stability analysis for linear discrete-time systems subject to actuator saturation

In this paper, stability of discrete-time linear systems subject to actuator saturation is analyzed by combining the saturation-dependent Lyapunov function method with Finsler’s lemma. New stability test conditions are proposed in the enlarged space containing both the state and its time difference which allow extra degree of freedom and lead to less conservative estimation of the domain of attraction. Furthermore, based on this result, a useful lemma and an iterative LMI-based optimization algorithm are also developed to maximize an estimation of domain of attraction. A numerical example illustrates the effectiveness of the proposed methods.     

Augmented Lyapunov functional approach for stability of neutral systems with mixed delays

This paper is concerned with the neutral‐delay‐dependent and discrete‐delay‐dependent stability for uncertain neutral systems with mixed delays and norm‐bounded uncertainties. Through constructing a new augmented Lyapunov‐Krasovskii functional and proving its positive definiteness, introducing some slack matrices and using integral inequality, the improved delay‐dependent stability criteria are derived in terms of linear matrix inequalities. Numerical examples are given to illustrate the significant improvement on the conservatism of the delay bound over some existing results. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

On stability and stabilisation for uncertain stochastic systems with time-delay and actuator saturation

This article concerns the stability analysis and design for uncertain stochastic systems with time-varying delays in state and actuator saturation. The parameter uncertainties belong to a convex polytopic set, and the delays are time varying. A sufficient condition is obtained in terms of a priori designed feedback matrix for determining if a given set is in inside the domain of attraction. Using the linear matrix inequality (LMI) approach, an estimate of the domain of attraction is presented. The problem of designing a state feedback controller such that the domain of attraction is enlarged is formulated through solving an optimisation problem with LMI constraints. A numerical example is given to illustrate the effectiveness of the proposed results.     

Stability analysis of a class of systems with parameter uncertainties and with state saturation nonlinearities

For linear systems with parameter uncertainties and subject to state saturation, we establish results concerning the global asymptotic stability of an equilibrium. In addition to providing a means for a qualitative analysis, these results also enable us to address the stabilizability of such systems by means of linear state feedback. Systems of the type considered herein capture two important phenomena commonly encountered in the modelling process: (i) system parameter uncertainties (which in the present case are modelled by means of interval matrices), and (ii) operation of systems over a wide range (which in the present case is accounted for by state saturation nonlinearities). We demonstrate the applicability of the present results by means of several specific examples.     

具有时变状态滞后的非线性2-D 离散系统的稳定性与控制

考虑一类由局部状态空间Fornasini-Marchesini(FM LSS)第二模型描述的,具有时变状态滞后非线性二维(2-D)离散系统的稳定性分析和控制问题.时变状态滞后项的上、下界为正整数,非线性项满足Lipschitz条件.首先,通过引入一个含有时滞上、下界的新Lyapunov函数,给出了系统的稳定性准则;然后设计了状态反馈控制器以保证系统的稳定性,进而,状态反馈控制律可由线性矩阵不等式求得;最后通过数值算例表明了所得结果的有效性.     

时延不确定离散时间系统的鲁棒跟踪控制

研究一类时延不确定离散时间系统的鲁棒跟踪控制问题．基于线性矩阵不等式(LMI)的控制方法，设计无记忆反馈控制器，构造了适用于时延不确定离散时间系统的Lyapunov函数．通过求解一个LMI便可得到控制器的增益矩阵，从而使系统的状态变量渐近跟踪预先设定的轨迹．仿真示例说明所提出的鲁棒跟踪控制算法是有效的．     

Switching signal design for asymptotic stability of uncertain multiple equilibrium switched systems with actuator saturation

This paper addresses the problem of robust control for a class of multiple equilibrium switched systems with actuator saturation and parameter uncertainties. The parameter uncertainties are described in norm‐bounded form. By combining the parametric Lyapunov equation approach and the gain‐scheduling technique, stabilization conditions are established in terms of linear matrix inequalities. State‐feedback controllers can be designed to guarantee the robust stability and performance of the closed‐loop system in the presence of parameter uncertainties and actuator saturation. The proposed method is to increase the convergence rate during the convergence of the states. Numerical examples and simulations are worked out to illustrate the feasibility of the proposed results. Copyright © 2015 John Wiley & Sons, Ltd.     

Reliable H-infinity filtering for linear systems with sensor saturation

In this paper, a new reliable H-infinity filter design problem is proposed for a class of continuous-time systems with sensor saturation and failures. Attention is focused on the analysis and synthesis problems of a full order reliable H-infinity filter such that the filtering error dynamics is asymptotically stable with a guaranteed disturbance rejection attenuation level γ. It is shown that the filtering error dynamics obtained from the original system plus the filter can be modeled by a linear system with sector bounded nonlinearity. The design conditions are given in terms of solutions to a set of linear matrix inequalities (LMIs). These conditions are then considered in a convex optimization problem with LMIs constraints in order to design an optimal reliable H-infinity filter. A numerical example is given to illustrate the effectiveness of the proposed results.     

Robust stabilization for uncertain discrete singular systems with state delay

The robust stabilization problem for uncertain discrete singular time‐delay systems is addressed in this paper. In terms of strict linear matrix inequality and a finite sum inequality, a delay‐dependent criterion for the nominal systems to be admissible is obtained. Based on the criterion, a state feedback controller, which guarantees that, for all admissible uncertainties, the resulting closed‐loop system is regular, causal and stable, is constructed. An explicit expression for the desired controller is also given. The obtained results include both delay‐independent and delay‐dependent cases. Some numerical examples are introduced to show the effectiveness of the given results. Copyright © 2008 John Wiley & Sons, Ltd.