An improved output feedback controller design for linear discrete-time systems using a matrix decomposition method

This paper presents the design of output feedback controllers for discrete-time (DT) linear systems. New sufficient LMI conditions are derived for designing static $H_2$ and $H_{\infty }$ controllers using decomposition of an auxiliary matrix. The decomposition facilitates linearization of nonlinear term of reduced size to obtain linear matrix inequality criteria. This leads to less conservative results as shown in the numerical examples. In addition, the proposed static output feedback criteria is also used for designing dynamic output feedback controllers for DT systems. Furthermore, a comparative study is also made for the proposed design method with the results existing in the literature. Finally, a DT static output feedback $H_{\infty }$ controller is designed for a quarter-car suspension system. Simulation results are provided to show the efficacy of the proposed design method.     

广义系统的时滞依赖静态输出反馈控制

针对一类不确定线性广义时滞系统,给出了静态输出反馈控制器的设计方法.首先基于标称广义时滞系统的稳定条件,以受限线性矩阵不等式形式,给出闭环广义时滞系统正则、无脉冲且渐近稳定的充分条件,同时利用受限矩阵不等式的可行解给出静态输出反馈控制律的一个参数化表示;其次,利用矩阵的正交补,把求受限线性矩阵不等式的可行解问题转化为求严格线性矩阵不等式(LMIs)的可行解;最后应用数值实例说明了所给方法的有效性和正确性.     

Unified stabilizing controller synthesis approach for discrete-time intelligent systems with time delays by dynamic output feedback

A novel model, termed the standard neural network model (SNNM), is advanced to describe some delayed (or non-delayed) discrete-time intelligent systems com- posed of neural networks and Takagi and Sugeno (T-S) fuzzy models. The SNNM is composed of a discrete-time linear dynamic system and a bounded static nonlinear operator. Based on the global asymptotic stability analysis of the SNNMs, linear and nonlinear dynamic output feedback controllers are designed for the SNNMs to stabilize the closed-loop systems, respectively. The control design equations are shown to be a set of linear matrix inequalities (LMIs) which can be easily solved by various convex optimization algorithms to determine the control signals. Most neural-network-based (or fuzzy) discrete-time intelligent systems with time delays or without time delays can be transformed into the SNNMs for controller synthesis in a unified way. Three application examples show that the SNNMs not only make controller synthesis of neural-network-based (or fuzzy) discrete-time intelligent systems much easier, but also provide a new approach to the synthesis of the controllers for the other type of nonlinear systems.     

New characterisations of positive realness and static output feedback control of discrete-time systems

This article is concerned with the problems of positive real analysis and control synthesis for discrete-time systems. New linear matrix inequality (LMI) characterisations of positive realness are derived, which enable one to check the positive realness by using parameter-dependent Lyapunov function. The relationship between the proposed characterisations and the existing ones are clarified, which shows that our new results are of less conservatism for characterising the positive realness of discrete-time systems with polytopic uncertainty. In addition, sufficient conditions for static output feedback positive real controller design are given in terms of solutions to a set of linear matrix inequalities. Numerical examples are included for illustration.     

Design of output feedback proportional–integral controller for polynomial fuzzy systems

In this paper, the design of dynamic output feedback control law for polynomial fuzzy systems is studied. The main purpose is to design a tracker control law for fuzzy polynomial systems that are subject to external bounded disturbances. The structure of the control law is considered as fuzzy proportional–integral control. The conditions for deriving the control law are formulated in the form of a sum of square (SOS) feasibility problem. The designed control law will be able to force the system state vector to follow the state vector of a stable reference model in addition to guaranteeing the $H_{\infty }$ performance measure. The simulation results show the efficiency of the proposed method exposed to external disturbance.     

Gain-scheduled output control design for a class of discrete-time nonlinear systems with saturating actuators

This paper deals with the stabilization of a class of nonlinear discrete-time systems under control saturations including time-varying parameter dependency. The control law studied consists of the gain-scheduled feedback of the measured output and of the nonlinearity present in the dynamics of the controlled system. Furthermore, the saturations are taken into account by modeling the nonlinear saturated system through a dead-zone nonlinearity satisfying a modified sector condition. Thus, as for precisely known systems, linear matrix inequality (LMI) stabilization conditions are proposed for such a generic system. These conditions can be cast into convex programming problems for design purposes. An illustrative example stresses the efficiency of the main result.     

Control of the INFANTE AUV using gain scheduled static output feedback

The paper describes the design and experimental testing of a control system for the INFANTE AUV in the horizontal plane. The methodology adopted for controller design is nonlinear gain scheduling control, whereby a set of linear finite static output feedback controllers are designed using linear matrix inequality (LMI)-based techniques and scheduled on the vehicle's forward speed. The paper summarizes the basic controller design steps, describes a technique for practical implementation of the nonlinear control system derived, and presents experimental results obtained with the AUV during tests at sea.     

L1 synthesis of a static output controller for positive systems by LMI iteration

An approach to find a static output feedback gain that makes the feedback system positive and minimizes the L₁ gain is proposed. The problem of finding a static output feedback gain has 3 aspects: stabilizing the system, making the system positive, and then minimizing the L₁ gain. Each subproblem is described by bilinear matrix inequality with respect to the feedback gain and the Lyapunov matrix or vector. Linear matrix inequality (LMI) that is sufficient to satisfy bilinear matrix inequality is derived using a convex‐concave decomposition, and the feedback gain sequence is calculated by an iterative solution of LMI. The sequence of the upper bounds on the design parameter is guaranteed to be monotonically nonincreasing for each algorithm. Similarly, 2 other LMIs are derived for each subproblem using another convex‐concave decomposition and PK iteration. The effectiveness of these algorithms is illustrated via several numerical examples.     

Static output feedback based fault accommodation design for continuous-time dynamic systems

This article addresses the integrated fault estimation (FE) and accommodation problem for continuous-time dynamic systems. First, using a specific system decomposition, we propose a new multi-objective reduced-order FE observer (RFEO), whose application range is wider than the existing adaptive and sliding mode ones. FE performances are further enhanced by introducing slack variables to reduce the conservatism generated by the direct design method. Finally, with the help of both system decomposition and slack variable techniques, a static output feedback fault tolerant controller (SOFFTC) design, whose sufficient condition is given in terms of linear matrix inequalities, is proposed to guarantee the stability of the closed-loop system in the presence of faults. Moreover, the RFEO and the SOFFTC are designed separately, so that their design parameters can be calculated easily. Simulation results of an aircraft application are presented to illustrate our contributions.     

Robustness of dynamic output feedback control for singular perturbation systems

The problem of the robustness of dynamic output feedback control for singular perturbation systems is investigated. The solution to this problem is reduced to the simultaneous design of static output feedback controllers for the fast subsystem and the so-called auxiliary system of the slow subsystem. Some conditions are proposed to ensure the robustness of the actual closed-loop system. The exact upper bound of the parasitic parameter for the controlled system is also determined. Finally, an actual model which failed in dynamic output feedback control in [4] is reexamined successfully here.     

Robust stabilization and guaranteed cost control for discrete-time linear systems by static output feedback

This paper proposes a systematic approach for the static output feedback control design for discrete-time uncertain linear systems. It is shown that if the open-loop system satisfies some particular structural conditions and the uncertainty has a specific structure, a static output feedback gain can be calculated easily, using a formula only involving the original system matrices. Among the conditions the system has to satisfy, the strongest one relies on a minimum phase argument. Square and nonsquare systems are considered. The performance problem through a quadratic criterion is also discussed (guaranteed cost control).     

Robust static output feedback control for linear discrete-time systems with time-varying uncertainties

This paper is concerned with the problem of designing robust static output feedback controllers for linear discrete-time systems with time-varying polytopic uncertainties. Sufficient conditions for robust static output feedback stabilizing controller designs are given in terms of solutions to a set of linear matrix inequalities, and the results are extended to H₂ and H_∞ static output feedback controller designs. Numerical examples are given to illustrate the effectiveness of the proposed design methods.     

不确定离散系统的输出反馈保性能控制

对一类具有范数有界时变参数不确定性的离散时间系统，研究设计一个输出反馈保性能控制器，使得闭环系统对所有允许的不确定性渐近稳定，且闭环性能指标值不超过某个确定的上界。基于线性矩阵不等式处理方法，证明了保性能控制器的存在性等价于一个线性矩阵不等式的可行性，并用该线性矩阵不等式的可解给出了控制器的构造方法和闭环性能指标的上界。     

Output feedback preview tracking control for discrete-time polytopic time-varying systems

This paper focuses on the problem of static output feedback preview tracking control for discrete-time systems with time-varying parameters subject to a previewable reference signal. We develop a design method of a robust controller with integral and preview actions achieving robust tracking performance. First, an augmented error system including future information on reference signal is constructed by introducing two new related auxiliary variables to the original system state and input. This leads to a tracking problem being transformed into a regulator problem. Then, a previewable reference signal is fully utilised through reformulation of the output equation for the augmented error system while considering a static output feedback. Meanwhile, the static output preview control gains are solved explicitly by the proposed conditions. Finally, a numerical example is given to demonstrate the effectiveness of the proposed method.     

Gain-scheduled, model-based anti-windup for LPV systems

The aim of this paper is to show that a recently proposed technique for anti-windup control of exponentially unstable plants can be easily extended to solve the corresponding robust anti-windup problem for linear parameter varying systems, for which the time varying parameters are measured online. The proposed technique is minimally conservative with respect to the size of the resulting operating region (which coincides, up to an arbitrarily small quantity, with the largest set on which asymptotic stability can be guaranteed for the considered plant with the given saturation level and uncertainty characteristics), and is not limited to plants having only small uncertainties or being open-loop stable.     

NN-adaptive output feedback tracking control for a class of discrete-time non-affine systems with a dynamic compensator

The problem of tracking control for a class of uncertain non-affine discrete-time nonlinear systems with internal dynamics is addressed. The fixed point theorem is first employed to ensure the control problem in question is solvable and well-defined. Based on it, an adaptive output feedback control scheme based on neural network (NN) is presented. The proposed control algorithm consists of two parts: a dynamic compensator is introduced to stabilise the linear portion of the tracking error system; a single-hidden-layer neural network (SHL NN) approximation mechanism is introduced to cancel the uncertainties resulting from the non-affine function, where the recursive weight update rules of NN estimation are derived from the discrete-time version of Lyapunov control theory. Ultimate boundedness of the error signals is shown through Lyapunov’s direct method and the discrete-time version of input-to-state stability (ISS) theory. Finally, a model of automatical underwater vehicle (AUV) is considered to show the effectiveness of the proposed control scheme.     

Smooth switching LPV controller design for LPV systems

This paper presents a method to design a smooth switching gain-scheduled linear parameter varying (LPV) controller for LPV systems. The moving region of the gain-scheduling variables is divided into a specified number of local subregions as well as subregions for the smooth controller switching, and one gain-scheduled LPV controller is assigned to each of the local subregions. For each switching subregion, a function interpolating two local LPV controllers associated with its neighborhood subregions is designed to satisfy the constraint of smooth transition of controller system matrices. The smooth switching controller design problem amounts to solving a feasibility problem which involves nonlinear matrix inequalities. To find a solution to the feasibility problem, an iterative descent algorithm which solves a series of convex optimization problems is proposed. The usefulness of the proposed controller design method is demonstrated with a control example of a flexible ball-screw drive system.     

Gain-scheduled L-one control for linear parameter-varying systems with parameter-dependent delays

This paper deals with the problem of gain-scheduled L-one control for linear parameter-varying (LPV) systems with parameter-dependent delays. The attention is focused on the design of a gain-scheduled L-one controller that guarantees being an asymptotically stable closed-loop system and satisfying peak-to-peak performance constraints for LPV systems with respect to all amplitude-bounded input signals. In particular, concentrating on the delay-dependent case, we utilize parameter-dependent Lyapunov functions (PDLF) to establish peak-to-peak performance criteria for the first time where there exists a coupling between a Lyapunov function matrix and system matrices. By introducing a slack matrix, the decoupling for the parameter-dependent time-delay LPV system is realized. In this way, the sufficient conditions for the existence of a gain-scheduled L-one controller are proposed in terms of the Lyapunov stability theory and the linear matrix inequality (LMI) method. Based on approximate basis function and the gridding technique, the corresponding controller design is cast into a feasible solution problem of the finite parameter linear matrix inequalities. A numerical example is given to show the effectiveness of the proposed approach.