Practical Stability Analysis and Synthesis of Linear Descriptor Systems with Disturbances

This paper considers the problems of practical stability analysis and synthesis of linear descriptor systems subject to timevarying and norm-bounded exogenous disturbances. A sufficient condition for the systems to be regular, impulsive-free and practically stable is derived. Then the synthesis problem is addressed and a state feedback controller is designed. To deal with the computational issue, the conditions of the main results are converted into linear matrix inequality （LMI） feasibility problems. Furthermore, two optimization algorithms are formulated to improve the system performances. Finally, numerical examples are given to illustrate the obtained results.

Static Output Feedback H_∞ Controllers Design for Descriptor Linear Systems Based on LMI

This paper considers the design problem of static output feedback H ∞ controllers for descriptor linear systems with linear matrix inequality (LMI) approach. Necessary and sufficient conditions for the existence of a static output feedback H ∞ controller are given in terms of LMIs. Furthermore, the design method of H ∞ controllers is provided using the solutions to the LMIs.

Eigenstructure Assignment in a Class of Second-order Descriptor Linear Systems: A Complete Parametric Approach

In this paper eigenstructure assignment via proportional-plus-derivative feedback is investigated for a class of second-order descriptor linear systems. Under certain conditions, simple, general and complete parametric solutions of both finite closed-loop eigenvector matrices and feedback gain matrices are derived. The parametric approach utilizes directly original system data, involves manipulations only on n-dimensional matrices, and reveals all the design degrees of freedom which can be further utilized to achieve certain additional system specifications. A numerical example shows the effect of the proposed approach.

Parametric Approach for the Normal Luenberger Function Observer Design in Second-order Descriptor Linear Systems

In this paper, the normal Luenberger function observer design for second-order descriptor linear systems is considered. It is shown that the main procedure of the design is to solve a so-called second-order generalized Sylvester-observer matrix equation. Based on an explicit parametric solution to this equation, a parametric solution to the normal Luenberger function observer design problem is given. The design degrees of freedom presented by explicit parameters can be further utilized to achieve some additional design requirements.

Robust model-reference control for descriptor linear systems subject to parameter uncertainties

Robust model-reference control for descriptor linear systems with structural parameter uncertainties is investigated. A sufficient condition for existing a model-reference zero-error asymptotic tracking controller is given. It is shown that the robust model reference control problem can be decomposed into two subproblems： a robust state feedback stabilization problem for descriptor systems subject to parameter uncertainties and a robust compensation problem. The latter aims to find three coefficient matrices which satisfy four matrix equations and simultaneously minimize the effect of the uncertainties to the tracking error. Based on a complete parametric solution to a class of generalized Sylvester matrix equations, the robust compensation problem is converted into a minimization problem with quadratic cost and linear constraints. A numerical example shows the effect of the proposed approach.

Robust Stabilization for Linear Time-varying Uncertain Periodic Descriptor Systems

这个问题赶出为线性变化时间的不明确的周期的描述符系统的稳定被重游。为线性变化时间的不明确的周期的描述符系统基于柔韧的稳定性的概念，为柔韧的稳定性的一个必要、足够的条件被提出。柔韧的稳定问题也被学习，相应必要、足够的条件用双系统的符号被给。获得的矩阵不平等条件能被转变到与一些免费矩阵的介绍的线性矩阵不平等一，它使分析和设计过程简单、可靠。

Singular linear quadratic performance with the worst disturbance rejection for descriptor systems

This paper deals with the problem of singular linear quadratic performance with the worst-disturbance rejection for descriptor systems. Under the conditions we give, the worst-disturbance and the optimal control-state pair are unique respectively, the optimal control can be synthesized as state feedback and the closed-loop system is regular, stable and impulse-free.

Observers for Descriptor Systems with Slope-restricted Nonlinearities

This paper addresses the observer design problem for a class of nonlinear descriptor systems whose nonlinear terms are slope-restricted. The full-order observer is formulated as a nonlinear descriptor system. A linear matrix inequality （LMI） condition is derived to construct the full-order observer. The existence and uniqueness of the solution to the obtained observer system are guaranteed. Furthermore, under the same LMI condition and a common assumption, a reduced-order observer is designed. Finally, the design methods are reduced to a strict LMI problem and illustrated by a numerical example.

基于直线段检测和LT描述符的矿井图像线特征匹配算法

图像匹配是同步定位与地图构建(SLAM)技术中极为重要的一环,用于根据图像之间的变换关系确定相机位姿。基于线特征的图像匹配方法具有较强的鲁棒性和抗噪能力,更加适用于井下图像匹配,基于深度学习的线描述符对线段遮挡等场景具有较高的鲁棒性,性能优于传统描述符,但卷积神经网络架构的描述符将可变长度线段抽象为固定维进行描述,不利于线段长度及视差变化较大图像的匹配。针对上述问题,提出一种基于直线段检测和线描述符的矿井图像线特征匹配算法。在频域利用单参数同态滤波降低图像的照射分量,并增强反射分量,提升亮度及对比度;在YUV空间利用对比度受限的自适应直方图均衡化(CLAHE)算法对亮度分量进行均衡,使亮度分布更加均匀;变换至RGB空间提取直线段检测(LSD)线,引入一种基于Transformer架构的LT描述符构建LSD线的特征向量,最后完成线特征匹配。实验结果表明:该算法结合了同态滤波和CLAHE算法的优点,增强后图像的亮度适中,对比度良好,灰度分布均匀,增强效果优于单参数同态滤波算法、EnlightenGAN算法;该算法提取的线特征数较原图平均提升了32.92%,在不同相似纹理占比、不同程度旋转与平移变化的井下图像匹配中鲁棒性好,平均正确匹配数为61.75对,平均精度为86.83%,优于线二进制描述符(LBD)算法、LBD_NNDR算法、LT算法,能够满足矿井图像稳健匹配的需求。

Passivity Control for Uncertain T-S Fuzzy Descriptor Systems

By means of matrix decomposition method a criterion is presented for the admissibility of T-S fuzzy descriptor system. Then, the problem of passivity control is studied for a kind of T-S fuzzy descriptor system with uncertain parameters, and sufficient conditions which make the closed-loop system admissible and strictly passive are obtained based on linear matrix inequality (LMI). The nonstrict LMIs restricted conditions which characterize the descriptor system are transformed into strict ones, so testing admissibility and passivity of the system can be finished simultaneously. The design scheme of state feedback controller is also obtained. Finally, a numerical example is given to show the validity and feasibility of the proposed approach.

Robust H_∞ control for uncertain descriptor systems with state and control delay

The problem of robust stabilization for uncertain continuous descriptor system with state and control delay is considered. The time-varying parametric uncertainty is assumed to be norm-bounded. The purpose of the robust stabilization is to design a memoryless state feedback law such that the resulting closed-loop system is robustly stable A sufficient condition that uncertain continuous descriptor system is robustly stabilizabled by state feedback law is derived in terms of linear matrix inequality （LMI）. Finally, a numerical example is provided to demonstrate the application of the proposed method.

Structural Characterization of Volatile Components of Rosa Banksiae Ait for Estimation and Prediction of Their Linear Retention Indices and Retention Times

The molecular electronegativity-distance vector （MEDV） was used to describe the molecular structure of volatile components of Rosa banksiae Ait, and QSRR model was built up by use of multiple linear regression （MLR）. Furthermore, in virtue of variable screening by the stepwise multiple regression technique, the QSRR models of 10 and 6 variables and linear retention index （LRI） 10, 7 and 6 varieables were built up by combinating MEDV with the Ultra2 column GC retention time （tR） of 53 volatile components of Rosa Banksiae Air. The multiple correlation coefficients （R） of modeling calculation values of QSRR model were 0.906, 0.906, 0.949, 0.943 and 0.949, respectively. The cross-verification multiple correlation coefficients （RCV） were 0.903, 0.904, 0.867, 0.901 and 0.904, respectively. The results show that the models constructed could provide estimation stability and favorable predictive ability.

A Descriptor System Approach of Sensor Fault State Estimation for Sampled-data Systems

This paper proposes a fault estimation method for sampled data systems with sensor faults. The sampled data system is firstly discretized to obtain a discrete time model. Then a descriptor system is constructed to describe the discretized system with sensor faults. Based on the descriptor system representation a bank of observers are designed to isolate and estimate the sensor faults. These observers can be synthesized by the linear matrix inequality (LMI) technique and sufficient conditions for the existence of these observers are derived. Finally the effectiveness is ascertained by an aircraft simulation example which is in the proposed method.

Stabilization and H-infinity control for interval descriptor systems

This paper considers H-infinity control problem for interval descriptor systems. Necessary and sufficient LMI-based conditions are derived for quadratic-like H-infinity control analysis of interval descriptor systems. Using the analysis result, two types of feedback controllers are designed so that the closed-loop interval descriptor systems are admissible with H-infinity-norm less than a prescribed value. To the best of the authors＇s knowledge, this is the first paper to deal with the H-infinity control problem of interval descriptor systems in the literature.

H-infinity control with an alpha-stability constraint:a descriptor system approach

This paper deals with the problem of designing state or full-order output feedback H-infinity controllers satisfying an α-stability constraint. A descriptor system approach is adopted to derive linear matrix inequality （LMI） conditions of α-stability and H-infinity performance for linear time-invariant （LTI） systems, under which the multiobjective control laws can be constructed with a mix of H-infinity performance and α-stability. Being expressed in terms of a group of bilinear matrix inequalities, the design algorithm is numerically tractable via an LMI optimization method. A numerical example illustrates the feasibility and effectiveness of the proposed approach, and the results are also compared with those obtained by the well-known Lyapunov shaping paradigm （LSP）.

Robust H_∞ control for fuzzy descriptor systems with state delay

The problem of robust H ∞ fuzzy state feedback control for uncertain fuzzy descriptor systems with state delay is solved. In the case that time-varying uncertainties are in all parameter matrices, sufficient conditions for the existence of fuzzy state feedback controller are presented in terms of linear matrix inequality (LMI). The proposed robust H ∞ control laws guarantee that the resulting closed-loop system is regular, impulse free, and stable with prescribed H ∞ norm bounded constraint for all admissible uncertainties. Finally, a numerical example is provided to demonstrate the validity of the proposed method.

Optimal guaranteed cost control for fuzzy descriptor systems with time-varying delay

Based on the delay-independent rule, the problem of optimal guaranteed cost control for a class of Takagi-Sugeno （T-S） fuzzy descriptor systems with time-varying delay is studied. A linear quadratic cost function is considered as the performance index of the closed-loop system. Sufficient conditions for the existence of guaranteed cost controllers via state feedback are given in terms of linear matrix inequalities （LMIs）, and the design of an optimal guaranteed cost controller can be reduced to a convex optimization problem. It is shown that the designed controller not only guarantees the asymptotic stability of the closed-loop fuzzy descriptor delay system, but also provides an optimized upper bound of the guaranteed cost. At last, a numerical example is given to illustrate the effectiveness of the proposed method and the perfect performance of the optimal guaranteed cost controller.

Observer-based passive control for descriptor systems with time-delay

This article is concerned with the problem of observer-based passive control for descriptor systems with time delay. Sufficient conditions are first presented for the closed loop systems to be admissible and passive with dissipation η in the case of that the time delay is known, and two kinds of methods are given to design the expected observer. Then, the case of that the time delay is unknown or uncertain is discussed. The observer-based control gains could be obtained from the solutions of linear matrix inequalities （LMIs）. Simulation examples are given to show the effectiveness of the designed methods.

New Approach to Stability Analysis and Stabilization of Discrete-Time T-S Fuzzy Descriptor Systems

The problems of stability and state feedback control for a class of discrete-time T-S fuzzy descriptor systems are investigated in this paper. Based on fuzzy Lyapunov function,a set of slack variables is introduced to remove the basic semi-definite matrix inequality condition to check the regularity,causality and stability of discrete-time T-S fuzzy descriptor systems; a new sufficient condition for the discrete-time T-S fuzzy descriptor systems to be admissible is proposed in terms of strict linear matrix inequalities( LMIs). And a sufficient condition is proposed for the existence of state feedback controller in terms of a set of coupled strict LMIs.Finally,an illustrative example is presented to demonstrate the effectiveness of the proposed approach.

Modeling of the Chemico-Physical Process of Protonation of Molecules Entailing Some Quantum Chemical Descriptors

Relying upon the basic tenets of scientific modeling, an ansatz for the evaluation of proton affinity of mole-cules are evolved in terms of a four component model. The components of the model chosen are global de-scriptors like ionization energies, global softness, electronegativity and electrophilicity index. These akin quantum mechanical descriptors of atoms and molecules are linked with the charge rearrangement and polarization that occur during the physico-chemical process of protonation of molecules. The suggested ansatz is invoked to compute the protonation energy of as many as 43 compounds of diverse physico-chemical nature viz, hydrocarbons, alcohols, carbonyls, carboxylic acids, esters, aliphatic amines and aromatic amines. A detailed comparative study of theoretically evaluated protonation energies of the above mentioned molecules vis-à-vis their corresponding experimental counterparts reveals that there is a close agreement between the theory and experiment. Thus the results strongly suggest that the proposed modeling and the ansatz for computing PA, the proton affinity, of molecules for studying the physico-chemical process of protonation may be valid proposition.