Robust Absolute Stability of General Interval Lur'e Type Nonlinear Control Systems

In this paper, Lyapunov function method is used to study the robust absolute stability of general interval Lur'e type nonlinear control systems. As a result, algebraically sufficient conditions with interval matrix inequality form are obtained for the general interval Lur'e type nonlinear control systems, thus the relationship between the stability of symmetrical interval matrix and the robust absolute stability of general interval Lur'e type nonlinear control systems is established.

Robust Stability Analysis of Smith Predictor Based Interval Fractional-Order Control Systems:A Case Study in Level Control Process

The robust stability study of the classic Smith predictor-based control system for uncertain fractional-order plants with interval time delays and interval coefficients is the emphasis of this work.Interval uncertainties are a type of parametric uncertainties that cannot be avoided when modeling real-world plants.Also,in the considered Smith predictor control structure it is supposed that the controller is a fractional-order proportional integral derivative(FOPID)controller.To the best of the authors'knowledge,no method has been developed until now to analyze the robust stability of a Smith predictor based fractional-order control system in the presence of the simultaneous uncertainties in gain,time-constants,and time delay.The three primary contributions of this study are as follows:ⅰ)a set of necessary and sufficient conditions is constructed using a graphical method to examine the robust stability of a Smith predictor-based fractionalorder control system—the proposed method explicitly determines whether or not the FOPID controller can robustly stabilize the Smith predictor-based fractional-order control system;ⅱ)an auxiliary function as a robust stability testing function is presented to reduce the computational complexity of the robust stability analysis;andⅲ)two auxiliary functions are proposed to achieve the control requirements on the disturbance rejection and the noise reduction.Finally,four numerical examples and an experimental verification are presented in this study to demonstrate the efficacy and significance of the suggested technique.

ON THE ROBUST STABILITY OF INTERVAL COEFFICIENTS NONLINEAR TIME-INVARIANT LARGE SCALE CONTINUOUS CONTROL SYSTEM WITH MULTI-GROUP MULTI-DELAY

In this paper, the result of the robust stability of interval coefficients nonlinear constant control system with multi-group multi-delay is given, by using the robust stability equivalent method.

Robust Stability Criteria for Neutral Systems with Interval Time-Varying Delays and Nonlinear Perturbations

This paper investigates the problem of delay-dependent robust stability analysis for a class of neutral systems with interval time-varying delays and nonlinear perturbations. Such nonlinear perturbations are with time-varying but norm-bounded characteristics. Based on a new Lyapunov-Krasovskii functional, together ,sith a free-weighting matrices technique, improved delay-dependent stability criteria are established. It is shown that less conservative results can be obtained in terms of linear matrix inequalities （LMIs）. Numerical examples are provided to demonstrate the effectiveness and less conservatism of the proposed approach.

ON THE UNCONDITIONAL ROBUST STABILITY FOR THE MULTIDELAYS INTERVAL COEFFICIENT CONTROL SYSTEM

In this paper, we are interested in the multigroup multidelays interval coefficient constant and time varying linear continuous control systems, by means of the equivalence method and the differential inequality in the time domain, we obtain some unconditional robust stability results for the multigroup multidelays constant and time-varying interval coefficient linear continuous control systems, respectively.

Adaptive Robust Servo Control for Vertical Electric Stabilization System of Tank and Experimental Validation

A tracking stability control problem for the vertical electric stabilization system of moving tank based on adaptive robust servo control is addressed.This paper mainly focuses on two types of possibly fast timevarying but bounded uncertainty within the vertical electric stabilization system:model parameter uncertainty and uncertain nonlinearity.First,the vertical electric stabilization system is constructed as an uncertain nonlinear dynamic system that can reflect the practical mechanics transfer process of the system.Second,the dynamical equation in the form of state space is established by designing the angular tracking error.Third,the comprehensive parameter of system uncertainty is designed to estimate the most conservative effects of uncertainty.Finally,an adaptive robust servo control which can effectively handle the combined effects of complex nonlinearity and uncertainty is proposed.The feasibility of the proposed control strategy under the practical physical condition is validated through the tests on the experimental platform.This paper pioneers the introduction of the internal nonlinearity and uncertainty of the vertical electric stabilization system into the settlement of the tracking stability control problem,and validates the advanced servo control strategy through experiment for the first time.

The Sufficient Conditions for Robust Absolute Stability of Lurie Control Systems

In this paper, the problem of absolute stability of continuous time with parametric nonlinear system uncertainty of a linear part and sector uncertainty of its nonlinear part is considered, the and sufficient conditions for absolute stability of direct and indirect control systems are presented. The corresponding results for robust absolute stability are improved.

Robust Adaptive Control of Nonholonomic Systems with Nonlinear Parameterization

全球适应的州的反馈控制策略与强壮的非线性的飘移和未知非线性的参数在锁住的形式为 nonholonomic 系统的一个类被介绍。一种参数分离技术被介绍把非线性的 parameterization nonholonomic 系统转变成一个象线性一样 parameterized nonholonomic 系统。然后，反馈支配设计被使用设计一个全球适应稳定控制器，切换的策略被开发消除 uncontrollability 的现象。建议控制器能保证那得到状态全球性集成到起源的所有系统，当另外的信号仍然保持围住时。模拟例子表明有效性和建议控制器的柔韧的特征。

Robust control of a class of non-affine nonlinear systems by state and output feedback

Robust control design is presented for a general class of uncertain non-affine nonlinear systems. The design employs feedback linearization, coupled with two high-gain observers: the first to estimate the feedback linearization error based on the full state information and the second to estimate the unmeasured states of the system when only the system output is available for feedback. All the signals in the closed loop are guaranteed to be uniformly ultimately bounded(UUB) and the output of the system is proven to converge to a small neighborhood of the origin. The proposed approach not only handles the difficulty in controlling non-affine nonlinear systems but also simplifies the stability analysis of the closed loop due to its linear control structure. Simulation results show the effectiveness of the approach.

Neural network based adaptive sliding mode control of uncertain nonlinear systems

The purpose of this paper is the design of neural network-based adaptive sliding mode controller for uncertain unknown nonlinear systems. A special architecture adaptive neural network, with hyperbolic tangent activation functions, is used to emulate the equivalent and switching control terms of the classic sliding mode control （SMC）. Lyapunov stability theory is used to guarantee a uniform ultimate boundedness property for the tracking error, as well as of all other signals in the closed loop. In addition to keeping the stability and robustness properties of the SMC, the neural network-based adaptive sliding mode controller exhibits perfect rejection of faults arising during the system operating. Simulation studies are used to illustrate and clarify the theoretical results.

Input-to-State Stabilization of Nonlinear Impulsive Delayed Systems: An Observer-Based Control Approach

This paper addresses the problems of input-to-state stabilization and integral input-to-state stabilization for a class of nonlinear impulsive delayed systems subject to exogenous dis-turbances.Since the information of plant’s states,time delays,and exogenous disturbances is often hard to be obtained,the key design challenge,which we resolve,is the construction of a state observer-based controller.For this purpose,we firstly propose a corresponding observer which is independent of time delays and exogenous disturbances to reconstruct(or estimate)the plant’s states.And then based on the observations,we establish an observer-based control design for the plant to achieve the input-to-state stability(ISS)and integral-ISS(iISS)properties.With the help of the comparison principle and average impulse interval approach,some sufficient conditions are presented,and moreover,two different linear matrix inequalities(LMIs)based criteria are proposed to design the gain matrices.Finally,two numerical examples and their simulations are given to show the effectiveness of our theoretical results.

Interval standard neural network models for nonlinear systems

A neural-network-based robust control design is suggested for control of a class of nonlinear systems. The design ap- proach employs a neural network, whose activation functions satisfy the sector conditions, to approximate the nonlinear system. To improve the approximation performance and to account for the parameter perturbations during operation, a novel neural network model termed standard neural network model (SNNM) is proposed. If the uncertainty is bounded, the SNNM is called an interval SNNM (ISNNM). A state-feedback control law is designed for the nonlinear system modelled by an ISNNM such that the closed-loop system is globally, robustly, and asymptotically stable. The control design equations are shown to be a set of linear matrix inequalities (LMIs) that can be easily solved by available convex optimization algorithms. An example is given to illustrate the control design procedure, and the performance of the proposed approach is compared with that of a related method reported in literature.

Solution of the HJI equations for nonlinear H_∞ control design by state-dependent Riccati equations approach

The relationship between the technique by state- dependent Riccati equations （SDRE） and Hamilton-Jacobi-lsaacs （HJI） equations for nonlinear H∞ control design is investigated. By establishing the Lyapunov matrix equations for partial derivates of the solution of the SDREs and introducing symmetry measure for some related matrices, a method is proposed for examining whether the SDRE method admits a global optimal control equiva- lent to that solved by the HJI equation method. Two examples with simulation are given to illustrate the method is effective.

Global robust stabilization of feedforward systems with uncertainties

This paper studies the global robust stabilization problem for a class of feedforward systems that is subject to both dynamic and time-varying static uncertainties. A small gain theorem-based bottom-up recursive design is developed for constructing a nested saturation control law. At each recursion, two versions of small gain theorem with restrictions are employed to establish the global attractiveness and local stability of the closed-loop system at the equilibrium point, respectively.

Semiglobal Stabilization via Output-feedback for a Class of Uncertain Nonlinear Systems

这份报纸为不明确的非线性的系统的一个班经由产量反馈认为 semiglobal 是稳定。与存在结果不同，在调查下面的系统拥有更严肃的非线性和实质地增加产量反馈的困难的未知控制系数控制器设计。联合 backstepping 方法和产量反馈支配途径，稳定控制器的 semiglobal 明确地被给，它能保证靠近环的系统在设计参数的适当选择下面完成 semiglobal asymptotic 稳定性。一个模拟例子验证理论结果和建议途径。

ROBUST ABSOLUTE STABILITY FOR INTERVAL YACUBOVICH TYPE CONTROL SYSTEM

Definition 1. If （?）A∈AI, the zero solution of（1.2 ）is absolutely stable, then we say the interval system （1.1）is Robust absolutely stable, which is denoted by （1.1）∈RAS. Definition 2. If （?）A∈AI, the zero solution of （1.2） is absolutely stable for partial variables xj0, …, xn+1, then we call the interval system （1.1）Robust absolutely stable for partial variables xj0, …, xn+1, which is denoted by （1.1）∈RAS （j0→n+1）.

Global stabilization by output feedback for a class of nonlinear systems with uncertain control coefficients and unmeasured states dependent growth

This paper considers the problem of global stabilization by output feedback for a class of nonlinear systems with uncertain control coefficients and with unmeasured states dependent growth. Mainly due to the uncertain control coefficients, the problem has remained unsolved and its major difficulty stems from the inapplicability of the commonly used high-gain like observer. By introducing an appropriate state transformation and a thoroughly novel observer based on high-gain K-filters, the backstepping design approach is successfully proposed to the output-feedback controller for this class of systems. It is shown that the global asymptotic stability of the closed-loop system can be guaranteed by the appropriate choice of the control parameters.

STATE-FEEDBACK ADAPTIVE STABILIZING CONTROL DESIGN FOR A CLASS OF HIGH-ORDER NONLINEAR SYSTEMS WITH UNKNOWN CONTROL COEFFICIENTS

In this paper, a new approach is successfully addressed to design the state-feedback adaptive stabilizing control law for a class of high-order nonlinear systems in triangular form and with unknown and nonidentical control coefficients, whose stabilizing control has been investigated recently under the knowledge that the lower bounds of the control coefficients are exactly known. In the present paper, without any knowledge of the lower bounds of the control coefficients, based on the adaptive technique and appropriately choosing design parameters, we give the recursive design procedure of the stabilizing control law by utilizing the approach of adding a power integrator together with tuning functions. The state-feedback adaptive control law designed not only preserves the equilibrium at the origin, but also guarantees the global asymptotic stability of the closed-loop states and the uniform boundedness of all the other closed-loop signals.

An all-coefficient adaptive control method for a class of nonlinear time-varying systems

In this paper, the extension of the all-coefficient adaptive control method to nonlinear time-varying systems is studied. A novel discretizing method is first proposed to derive the discrete-time model for a class of nonlinear time-varying systems. The characteristics of the coefficients of the discrete-time model are derived by this method, based on which the all-coefficient adaptive control method is given for the class of nonlinear time-varying systems. Sufficient conditions on the closed-loop stability are given. Simulations show the purposed adaptive control method can achieve satisfying performance. Finally further discussion on applying low-order all-coefficient adaptive control method to high order nonlinear time-varying system is given.