On the Input—Output Decoupling of 2-D Systems by State Feedback

The problem of designing a linear state feedback controller for single-input single-output decoupling of linear multivariable 2-D (two-dimensional) systems is discussed. A method is presented for the determination of the decoupling controller matrices which, when applied to the open-loop system, yield a closed-loop system whose transfer function matrix is diagonal and nonsingular. Necessary and sufficient conditions are established for the state feedback decoupling problem to have a solution. Two examples are included to illustrate the proposed decoupling method.     

Exact Model-Matching of 2-D Systems via State Feedback

This paper considers the problem of matching the transfer function matrix of a given two-dimensional (2-D) system to that of a desired 2-D model using state feedback. The approach followed refers to systems having square transfer function matrices and reduces the problem to that of solving a linear system of equations. Furthermore, necessary and sufficient conditions are established for exact matching. An example is included to illustrate the proposed method.     

State feedback uniform decoupling problem of linear time-varying analytic systems

A new approach to the input-output uniform decoupling problem of linear time-varying analytic systems via proportional state feedback is presented. A major feature of the proposed approach is that it reduces the solution of the uniform decoupling problem to that of solving a linear algebraic system of equations. This system of equations greatly facilitates the solution of the three major aspects of the decoupling problem: the necessary and sufficient conditions, the general analytical expressions for the controller matrices, and the structure of the uniformly decoupled closed-loop system.     

Delay-dependent guaranteed cost control for uncertain 2-D discrete systems with state delay in the FM second model

This paper is concerned with the problem of delay-dependent guaranteed cost control for uncertain two-dimensional (2-D) state delay systems described by the Fornasini and Marchesini (FM) second state-space model. Given a scalar α∈(0,1), a sufficient condition for the existence of delay-dependent guaranteed cost controllers is given in terms of a linear matrix inequality (LMI) based on a summation inequality for 2-D discrete systems. A convex optimization problem is proposed to design a state feedback controller stabilizing the 2-D state delay system as well as achieving the least guaranteed cost for the resulting closed-loop system. Finally, the simulation example of thermal processes is given to illustrate the effectiveness of the proposed result.     

Model transformation based sliding mode control of discrete-time two-dimensional Fornasini–Marchesini systems

This paper investigates the problem of sliding mode control (SMC) for discrete-time two-dimensional (2-D) systems subject to external disturbances. Given a 2-D Fornasini–Marchesini (FM) local state space model, attention is focused on designing the 2-D sliding surface and sliding mode controller, which guarantees the resultant closed-loop system to be asymptotically stable. Particularly, this problem is solved using the model transformation based method. First of all, sufficient conditions are formulated for the existence of a linear sliding surface guaranteeing the asymptotic stability of the equivalent sliding mode dynamics. Based on this, a sliding mode controller is synthesized to ensure that the associated 2-D FM system satisfies the reaching condition. The efficiency of the proposed 2-D SMC law design is shown by a numerical example. This paper extends the idea of model transformation to the 2-D systems and solves the SMC problem of a more general 2-D model in FM type for the first time.     

二阶系统数值解耦方法的研究

数值代数领域通过保持Lancaster结构来研究二阶系统的解耦问题,但寻找解耦变换涉及到了非线性方程组求解问题,难以实现. 提出了一种二阶系统数值解耦的新方法. 根据系统解耦前后的同谱信息确定解耦后的系统,将寻找解耦变换的非线性问题转化为齐次Sylvester方程求解问题; 并利用矩阵的Kronecker积理论求解二阶系统的解耦变换. 数值试验证明了该方法的可行性,为二阶系统的数值解耦找到了更便易的实现途径.     

Modeling and stabilization of a wireless network control system with packet loss and time delay

The problem of modeling and stabilization of a wireless network control system (NCS) is considered in this paper, where packet loss and time delay exist simultaneously in the wireless network. A discrete-time switched system with time-varying delay model is first proposed to describe the system closed by a static state feedback controller. A sufficient criteria for the discrete-time switched system with time-varying delay to be stable is proposed, based on which, the corresponding state feedback controller is obtained by solving a set of linear matrix inequalities (LMIs). Numerical examples show the effectiveness of the proposed method.     

随机时滞非线性系统状态反馈镇定

针对一类严格反馈随机时滞非线性系统，提出了一种状态反馈镇定方案。在系统非线性函数满足线性增长条件的假设下，基于反推技术和占优方法设计了一个无记忆线性状态反馈控制器。通过构建一个四次Lyapunov-Krasoviskii泛函，证明了闭环系统在概率意义下全局渐近稳定，仿真实例说明了方案的可行性。     

Sufficient and necessary conditions for stabilizing singular fractional order systems with partially measurable state

This paper is concerned with the stabilization problem of singular fractional order systems with order α?∈?(0, 2). In addition to the sufficient and necessary condition for observer based control, a sufficient and necessary condition for output feedback control is proposed by adopting matrix variable decoupling technique. The developed results are more general and efficient than the existing works, especially for the output feedback case. Finally, two illustrative examples are given to verify the effectiveness and potential of the proposed approaches.     

Controller design for 2-D stochastic nonlinear Roesser model: A probability-dependent gain-scheduling approach

This note is concerned with the static output feedback control problem for two-dimensional (2-D) uncertain stochastic nonlinear systems. The systems under consideration are subjected to time delays, multiplicative noises and randomly occurring missing measurements. A random variable sequence following the Bernoulli distribution with time-varying probability is employed to character the missing measurements which are assumed to occur in a random way. A new gain-scheduling method based on the time-varying probability parameter is proposed to accomplish the design task. By constructing a suitable Lyapunov functional, sufficient conditions to guarantee the systems to be mean-square asymptotically stable are established. The addressed 2-D controller design problem can be reduced to a convex optimization problem by some mathematical techniques. In the last section, a numerical example and the comparative analysis are provided to illustrate the efficiency of our proposed design approach.     

A general theory of decoupling a system of lossless coupled lines using linear transformations

This paper presents a general theory of decoupling a system of nonuniform lossless coupled lines with the aid of linear transformations. The lines have a common return and support only TEM waves. It is shown that the solution of the decoupling problem is equivalent to that of the simultaneous diagonalization of a set of real constant matrices through specially related pairs of congruent and similarity transformations. The solution of the equivalent problem yields the necessary and sufficient conditions for decoupling the system of coupled lines. A systematic procedure for decoupling is then presented. A special case is studied for which the decoupling problem becomes simpler. Finally, we have derived a set of equivalent but considerably simpler necessary and sufficient conditions for decoupling the frequently used system of a pair of lossless coupled lines.     

Performance-oriented parallel distributed compensation

The main idea of the original parallel distributed compensation (PDC) method is to partition the dynamics of a nonlinear system into a number of linear subsystems, design a number of state feedback gains for each linear subsystem, and finally generate the overall state feedback gain by fuzzy blending of such gains. A new modification to the original PDC method is proposed here, so that, besides the stability issue, the closed-loop performance of the system can be considered at the design stage. For this purpose, the state feedback gains are not considered constant through the linearized subsystems, rather, based on some prescribed performance criteria, several feedback gains are associated to every subsystem, and the final gain for every subsystem is obtained by fuzzy blending of such gains. The advantage is that, for example, a faster response can be obtained, for a given bound on the control input. Asymptotic stability of the closed loop system is also guaranteed by using the Lyapunov method. To illustrate the effectiveness of the new method, control of a flexible joint robot (FJR) is investigated and superiority of the designed controller over other existing methods is demonstrated.     

Robust observer-based fault estimation and accommodation of discrete-time piecewise linear systems

In this paper a new integrated observer-based fault estimation and accommodation strategy for discrete-time piecewise linear (PWL) systems subject to actuator faults is proposed. A robust estimator is designed to simultaneously estimate the state of the system and the actuator fault. Then, the estimate of fault is used to compensate for the effect of the fault. By using the estimate of fault and the states, a fault tolerant controller using a PWL state feedback is designed. The observer-based fault-tolerant controller is obtained by the interconnection of the estimator and the state feedback controller. We show that separate design of the state feedback and the estimator results in the stability of the overall closed-loop system. In addition, the input-to-state stability (ISS) gain for the closed-loop system is obtained and a procedure for minimizing it is given. All of the design conditions are formulated in terms of linear matrix inequalities (LMI) which can be solved efficiently. Also, performance of the estimator and the state feedback controller are minimized by solving convex optimization problems. The efficiency of the method is demonstrated by means of a numerical example.     

Feedback factorizing control of 3-D transfer functions via a canonical state-space model

The problem factorizing (separating) the transfer function of a given SISO 3-D discrete system, ie of a system depending on three independent variables, is considered. The 3-D system is assumed to be available in its transfer function representation, which is converted to a canonical state-space model by a simple inspection procedure. Then applying state-feedback to this canonical model we choose the feedback matrix gain (under certain conditions) such that the transfer function of the closed-loop system has the desireed factorized form, ie a product of three 1-D transfer functions each one being dependent on a single variable. The method is illustrated by a nontrivial numerical example.     

Robust stabilization of uncertain 2-D discrete-time delayed systems using sliding mode control

This paper aims to solve the problem of sliding mode control for an uncertain two-dimensional (2-D) systems with states having time-varying delays. The uncertainties in the system dynamics are constituted of mismatched uncertain parameters and the unknown nonlinear bounded function. The proposed problem utilizes the model transformation approach. By segregating the proper Lyapunov–Krasovskii functional in concert with the improved version of Wirtinger-based summation inequality, sufficient solvability conditions for the existence of linear switching surfaces have been put forward, which ensure the asymptotical stability of the reduced-order equivalent sliding mode dynamics. Then, we solve the controller synthesis problem by extending the recently proposed reaching law to 2-D systems, whose proportional part is appropriately scaled by the factor that does not depend on some constant terms but rather on current switching surface’s value, which in turn ensures the faster convergence and better robustness against uncertainties. Finally, the proposed results have been validated through an implementation to a suitable physical system.     

Finding exact periodic solutions in Lure systems through periodic signal mapping

A solution of the periodic problem in a nonlinear system comprising a single-valued symmetric nonlinearity (Lure system) and linear dynamics is presented. The solution is designed as an iterative application of Periodic Signal Mapping to refine the approximate solution obtained through the describing function method. The algorithm is based upon the transformation of the original nonlinear system into an equivalent nonlinear system for which the filtering hypothesis is satisfied exactly, and for that reason the latter being suitable for application of the developed algorithm. The solution sought for is a fixed point of the periodic signal mapping. Conditions of asymptotic convergence of the proposed algorithm are given. The proposed approach is illustrated by two examples of analysis of periodic motions in a relay feedback system and chattering in a terminal sliding mode.     

Distributed event-triggered control co-design for large-scale systems via static output feedback

This work investigates the problem of distributed control for large-scale systems, in which a communication network is available to exchange information. To avoid the unnecessary communication, an event-triggered control (ETC) mechanism is introduced, in which the transmission occurs only when a certain event is triggered. Under the assumption that only the output signal is available, the static output feedback (SOF) is considered in this work. The aim of the co-design is to design an SOF controller and an ETC condition simultaneously such that the overall closed-loop system is stabilized with a certain level of performance. To this end, an event-triggering scheme based on output signals is proposed to determine when the event is triggered. Then the closed-loop system is modeled as a linear perturbed system. The distributed control co-design is formulated as a convex optimization problem with linear matrix inequalities (LMIs) constraints. Finally, a numerical example is presented to show the effectiveness of the proposed design method.     

Iterative learning feedback control for linear parabolic distributed parameter systems with multiple collocated piecewise observation

This paper presents a novel iterative learning feedback control method for linear parabolic distributed parameter systems with multiple collocated piecewise observation. Multiple actuators and sensors distributed at the same position of the spatial domain are utilized to perform collocated piecewise control and measurement operations. The advantage of the proposed method is that it combines the iterative learning algorithm and feedback technique. Not only can it use the iterative learning algorithm to track the desired output trajectory, but also the feedback control approach can be utilized to achieve real-time online update. By utilizing integration by parts, triangle inequality, mean value theorem for integrals and Gronwall lemma, two sufficient conditions based on the inequality constraints for the convergence analysis of the tracking error system are presented. Some simulation experiments are provided to prove the effectiveness of the proposed method.     

Dynamic output feedback sliding mode control for spacecraft hovering without velocity measurements

In consideration of target angular velocity uncertainty and external disturbance, a modified dynamic output feedback sliding mode control (DOFSMC) method is proposed for spacecraft autonomous hovering system without velocity measurements. As a stepping-stone, an additional dynamic compensator is introduced into the design of sliding surface, then an augmented system is reconstructed with the system uncertainty and external disturbance. Based on the linear matrix inequality (LMI), a sufficient condition is given, which guarantees the disturbance attenuation performance of sliding mode dynamics. By introducing an auxiliary variable, a modified version of adaptive sliding mode control (ASMC) law is designed, and the finite-time stability of sliding variable is established by the Lyapunov stability theory. Compared with other results, the proposed method is less conservative and can decrease the generated control input force significantly. Finally, two simulation examples are performed to validate the effectiveness of the proposed method.