An antiwindup approach to enlarging domain of attraction for linearsystems subject to actuator saturation

The article considers linear systems subject to actuator saturation. An antiwindup technique is used to enlarge the domain of attraction of the closed-loop system under an a priori designed linear dynamic feedback law. The design of the antiwindup compensation gain is formulated and solved as an iterative optimization problem with LMI constraints. Numerical examples are used to demonstrate the effectiveness of the proposed design technique     

Stability analysis and anti-windup design of switched systems with actuator saturation

The stability analysis and anti-windup design problem is investigated for two linear switched systems with saturating actuators by using the single Lyapunov function approach. Our purpose is to design a switching law and the anti-windup compensation gains such that the maximizing estimation of the domain of attraction is obtained for the closed-loop system in the presence of saturation. Firstly, some sufficient conditions of asymptotic stability are obtained under given anti-windup compensation gains based on the single Lyapunov function method. Then, the anti-windup compensation gains as design variables are presented by solving a convex optimization problem with linear matrix inequality (LMI) constraints. Two numerical examples are given to show the effectiveness of the proposed method.     

Stability Analysis and Design of Uncertain Discrete‐time Switched Systems with Actuator Saturation Using Antiwindup and Multiple Lyapunov Functions Approach

The stability analysis and anti‐windup design problem is investigated for a class of discrete‐time switched systems with saturating actuators by using the multiple Lyapunov functions approach. Firstly, we suppose that a set of linear dynamic output controllers have been designed to stabilize the switched system without input saturation. Then, we design anti‐windup compensation gains and a switching law in order to enlarge the domain of attraction of the closed‐loop system. Finally, the anti‐windup compensation gains and the estimation of domain of attraction are presented by solving a convex optimization problem with linear matrix inequality (LMI) constraints. A numerical example is given to demonstrate the effectiveness of the proposed design method.     

Antiwindup design with guaranteed regions of stability: an LMI-based approach

This note addresses the design of antiwindup gains for obtaining larger regions of stability for linear systems with saturating inputs. Considering that a linear dynamic output feedback has been designed to stabilize the linear system (without saturation), a method is proposed for designing an antiwindup gain that maximizes an estimate of the basin of attraction of the closed-loop system. It is shown that the closed-loop system obtained from the controller plus the antiwindup gain can be modeled by a linear system with a deadzone nonlinearity. A modified sector condition is then used to obtain stability conditions based on quadratic Lyapunov functions. Differently from previous works these conditions are directly in linear matrix inequality form. Some numerical examples illustrate the effectiveness of the proposed design technique when compared with the previous ones.     

Antiwindup for stable linear systems with input saturation: an LMI-based synthesis

This paper considers closed-loop quadratic stability and L/sub 2/ performance properties of linear control systems subject to input saturation. More specifically, these properties are examined within the context of the popular linear antiwindup augmentation paradigm. Linear antiwindup augmentation refers to designing a linear filter to augment a linear control system subject to a local specification, called the "unconstrained closed-loop behavior." Building on known results on H/sub /spl infin// and LPV synthesis, the fixed order linear antiwindup synthesis feasibility problem is cast as a nonconvex matrix optimization problem, which has an attractive system theoretic interpretation: the lower bound on the achievable L/sub 2/ performance is the maximum of the open and unconstrained closed-loop L/sub 2/ gains. In the special cases of zero-order (static) and plant-order antiwindup compensation, the feasibility conditions become (convex) linear matrix inequalities. It is shown that, if (and only if) the plant is asymptotically stable, plant-order linear antiwindup compensation is always feasible for large enough L/sub 2/ gain and that static antiwindup compensation is feasible provided a quasi-common Lyapunov function, between the open-loop and unconstrained closed-loop, exists. Using the solutions to the matrix feasibility problems, the synthesis of the antiwindup augmentation achieving the desired level of L/sub 2/ performance is then accomplished by solving an additional LMI.     

Anti-windup design of uncertain discrete-time Markovian jump systems with partially known transition probabilities and saturating actuator

This paper carries out a study on the design of anti-windup gains for uncertain discrete-time Markovian jump systems subject to both actuator saturation and partially known transition probabilities. The parameter uncertainties appearing in both the state and input matrices are assumed to be time-varying and norm-bounded. Under the assumption that a set of linear dynamic output feedback controllers have been designed to stabilise the Markovian jump system in the absence of actuator saturation, anti-windup compensation gains are designed for maximising the domain of attraction of the closed-loop system with actuator saturation. Then, by solving a convex optimisation problem with constraints of a set of linear matrix inequalities, the anti-windup compensation gains are obtained. A simulation example is provided to illustrate the effectiveness of the proposed technique.     

L 2-gain analysis and anti-windup design of discrete-time switched systems with actuator saturation

This paper investigates L2-gain analysis and anti-windup compensation gains design for a class of discrete-time switched systems with saturating actuators and L2 bounded disturbances by using the switched Lyapunov function approach.For a given set of anti-windup compensation gains,we firstly give a sufficient condition on tolerable disturbances under which the state trajectory starting from the origin will remain inside a bounded set for the corresponding closed-loop switched system subject to L2 bounded disturbances.Then,the upper bound on the restricted L2-gain is obtained over the set of tolerable disturbances.Furthermore,the antiwindup compensation gains aiming to determine the largest disturbance tolerance level and the smallest upper bound of the restricted L2-gain are presented by solving a convex optimization problem with linear matrix inequality(LMI) constraints.A numerical example is given to illustrate the effectiveness of the proposed design method.     

Robust stabilization of switched discrete-time systems with actuator saturation

This paper studies the robust stabilization problem of switched discrete-time linear systems subject to actuator saturation. New switched saturation-dependent Lyapunov functions are exploited to design a robust stabilizing state feedback controller that maximizes an estimation of the domain of attraction. The design problem of controller （coefficient matrices） is then reduced to an optimization problem with linear matrix inequality （LMI） constraints. A numerical example is given to show the effectiveness of the proposed method.     

Design of switched linear systems in the presence of actuator saturation and L-infinity disturbances

This paper considers the problem of disturbance tolerance/rejection of a switched system resulting from a family of linear systems subject to actuator saturation and L-infinity disturbances. For a given set of linear feedback gains, a given switching scheme and a given bound on the L-infinity norm of the disturbances, conditions are established, in terms of linear or bilinear matrix inequalities, under which a set of a certain form is invariant for a given switched linear system in the presence of actuator saturation and L-infinity disturbances, and the closed-loop system possesses a certain level of disturbance rejection capability. With these conditions, the design of feedback gains and switching scheme can be formulated and solved as constrained optimization problems. Disturbance tolerance is measured by the largest bound on the disturbances for which the trajectories starting from a given set remain bounded. Disturbance rejection is measured either by the L-infinity norm of the system output or by the system’s ability to steer its state into and/or keep it within a small neighborhood of the origin. In the event that all systems in the family are identical, the switched system reduces to a single system under a switching feedback law. Simulation results show that such a single system under a switching feedback law could have stronger disturbance tolerance/rejection capability than a single linear feedback law can.     

Nonfragile robust exponential stabilization of nonlinear uncertain switched systems with actuator saturation

For nonlinear uncertain switched systems, the problem of how to overcome the controller vulnerability is studied when the actuator saturation is considered. The sufficient condition for guaranteeing nonfragile robust exponential stabilization of the system is derived by using the method of minimum dwell time. Then, a switching law and the nonfragile state feedback controllers are designed such that the closed-loop system can be robustly exponentially stabilized at the origin. Next, when some scalar parameters of the closed-loop system are given, the design issue of the nonfragile state feedback controllers, which aim at enlarging the estimation of domain of attraction for closed-loop system, is transformed into a convex optimization issue with linear matrix inequalities (LMI) constraints. Finally, an example is given to verify the effectiveness of the proposed method.     

Analysis and design of discrete-time linear systems with nested actuator saturations

This paper is concerned with the analysis and design of discrete-time linear systems subject to nested saturation functions. By utilizing a new compact convex hull representation of the saturation nonlinearity, a linear matrix inequalities (LMIs) based condition is obtained for testing the local and global stability of the considered nonlinear system. The estimation of the domain of attraction and the design of feedback gains such that the estimation of the domain of attraction for the resulting closed-loop system is maximized are then converted into some LMIs based optimization problems. Compared with the existing results on the same problems, the proposed solutions are less conservative as more slack variables are introduced into the conditions. A couple of numerical examples are worked out to validate the effectiveness of the proposed approach.     

Anti-windup strategies for discrete-time switched systems subject to input saturation

This paper deals with the design of anti-windup compensator for discrete-time switched systems subject to input saturation. The cases of static and dynamic anti-windup controllers are addressed aiming at maximising the estimate of the basin of attraction of the origin for the closed-loop system. Two aspects of the switching law are taken into account during the design: either it is arbitrary or it is a part of the complete control law. Theoretical conditions allowing to synthesise the anti-windup compensator are mainly described through linear matrix inequalities. Computational oriented conditions are then provided to solve convex optimisation problems that are able to give a constructive solution.     

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.     

Robust Control for a Class of Uncertain Switched Fuzzy Systems with Saturating Actuators

This paper investigates the robust control problem for a class of uncertain switched fuzzy systems with saturating actuators. The asymptotical stability for fuzzy subsystems subject to actuator saturation is not assumed. Based on the multiple Lyapunov functions method, we design a switching law and a state feedback control law such that the closed‐loop system is asymptotically stable. Additionally, the estimation of the domain of attraction is presented by solving an optimization problem. Finally, simulation results verify the feasibility and effectiveness of the proposed method.     

An analysis and design method for discrete-time linear systems under nested saturation

This paper considers a discrete-time linear system under nested saturation. Nested saturation arises, for example, in systems with actuators subject to both magnitude and rate saturation. A condition is derived in terms of a set of auxiliary feedback gains for determining if a given ellipsoid is contractively invariant. Moreover, this condition is shown to be equivalent to linear matrix inequalities (LMIs) in the actual and auxiliary feedback gains. As a result, the estimation of the domain of attraction for a given set of feedback gains is then formulated as an optimization problem with LMI constraints. By viewing the feedback gains as extra free parameters, the optimization problem can be used for controller design.     

An analysis and design method for linear systems under nested saturation

This paper considers a linear system under nested saturation. Nested saturation arises, for example, when the actuator is subject to magnitude and rate saturation simultaneously. A condition is derived in terms of a set of auxiliary feedback gains for determining if a given ellipsoid is contractively invariant. Moreover, this condition is shown to be equivalent to linear matrix inequalities (LMIs) in the actual and auxiliary feedback gains. As a result, the estimation of the domain of attraction for a given set of feedback gains can be formulated as an optimization problem with LMI constraints. By viewing the feedback gains as extra free parameters, the optimization problem can be used for controller design.     

Output Feedback Stabilization of Linear Systems With Actuator Saturation

The note presents a method for designing an output feedback law that stabilizes a linear system subject to actuator saturation with a large domain of attraction. This method applies to general linear systems including strictly unstable ones. A nonlinear output feedback controller is first expressed in the form of a quasi-LPV system. Conditions under which the closed-loop system is locally asymptotically stable are then established in terms of the coefficient matrices of the controller. The design of the controller (coefficient matrices) that maximizes an estimate of the domain of attraction is then formulated and solved as an optimization problem with LMI constraints     

不确定离散切换系统具有极点约束的保性能控制

对一类含有范数有界不确定性的离散切换系统和一个二次型性能指标，研究其具有闭环极点约束的鲁棒状态反馈保性能控制问题．利用二次Lyapunov函数方法和线性矩阵不等式技术，给出了鲁棒保性能控制器存在的一个充分条件，在所构造切换规则下，闭环系统二次D稳定，且满足给定的性能指标．在此基础上，将次优保性能控制器设计问题转化为一组线性矩阵不等式约束下的凸优化问题．数值例子说明了所提方法的有效性．     

带有饱和执行器的T-S离散模糊系统的LQ模糊控制

研究了带有饱和执行器的Takagi-SugenoT-S离散模糊系统的LQ模糊控制问题,利用Lyapunov稳定理论、PDC(平行分配补偿)技术以及线性矩阵不等式方法,得到了闭环模糊系统的渐近稳定的充分条件,给出了闭环系统的LQ模糊控制律的设计方法和吸引域的一个估计,并建立了闭环系统的LQ性能函数上界的计算公式.进一步,针对两类优化问题,即:LQ性能最小化问题和吸引域最大化问题,给出了相应的带有线性矩阵不等式约束的计算方法.最后,一个仿真例子说明了所给方法的有效性.     

PID Control of Planar Nonlinear Uncertain Systems in the Presence of Actuator Saturation

This paper investigates PID control design for a class of planar nonlinear uncertain systems in the presence of actuator saturation. Based on the bounds on the growth rates of the nonlinear uncertain function in the system model, the system is placed in a linear differential inclusion. Each vertex system of the linear differential inclusion is a linear system subject to actuator saturation. By placing the saturated PID control into a convex hull formed by the PID controller and an auxiliary linear feedback law, we establish conditions under which an ellipsoid is contractively invariant and hence is an estimate of the domain of attraction of the equilibrium point of the closed-loop system. The equilibrium point corresponds to the desired set point for the system output. Thus, the location of the equilibrium point and the size of the domain of attraction determine, respectively, the set point that the output can achieve and the range of initial conditions from which this set point can be reached. Based on these conditions, the feasible set points can be determined and the design of the PID control law that stabilizes the nonlinear uncertain system at a feasible set point with a large domain of attraction can then be formulated and solved as a constrained optimization problem with constraints in the form of linear matrix inequalities (LMIs). Application of the proposed design to a magnetic suspension system illustrates the design process and the performance of the resulting PID control law.