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On the Coefficients of Polynomials with Positive Real Part in the Unit Disk
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作者 申大维 《Journal of Beijing Institute of Technology》 EI CAS 1995年第2期110+106-110,共6页
Let Q be the class of real coefficient polynomials of degree 2 with positive real part in the unit disk and constant term equal to 1. aam coefficient region of polynomials in Q is found and some sharp coefficient esti... Let Q be the class of real coefficient polynomials of degree 2 with positive real part in the unit disk and constant term equal to 1. aam coefficient region of polynomials in Q is found and some sharp coefficient estimates for the polynomials with positive real part in the unit disk are established in this paper. 展开更多
关键词 POLYNOMIALS coefficients/positive real part SUBORDINATION
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THE EXTREME POINTS OF A CLASS OF ANALYTIC FUNCTIONS WITH POSITIVE REAL PART AND A PRESCRIBED SET OF VALUES 被引量:1
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作者 彭志刚 《Acta Mathematica Scientia》 SCIE CSCD 2012年第5期1929-1936,共8页
Letζ =(0,z1,z2,···,zn) with |zj|〈1for1≤j≤n,ω=(1,w1,w2,···,wn),and P(ζ,ω) denote the set of functions p(z) that are analytic in D={z:|z|〈1} and satisfy Rep(z)〉0(|... Letζ =(0,z1,z2,···,zn) with |zj|〈1for1≤j≤n,ω=(1,w1,w2,···,wn),and P(ζ,ω) denote the set of functions p(z) that are analytic in D={z:|z|〈1} and satisfy Rep(z)〉0(|z|〈1),p(0)=1,p(zj)=wj,j=1,2,···,n.In this article we investigate the extreme points of P(ζ,ω). 展开更多
关键词 extreme point positive real part Blaschke product
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A Certain Subclass of Analytic Functions with Bounded Positive Real Part 被引量:2
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作者 Young Jae Sim Oh Sang Kwon 《Advances in Pure Mathematics》 2013年第4期409-414,共6页
For real numbers α and β such that 0≤α<1<β, we denote by T(α,β) the class of normalized analytic functions which satisfy , where U denotes the open unit disk. We find some relationships involving function... For real numbers α and β such that 0≤α<1<β, we denote by T(α,β) the class of normalized analytic functions which satisfy , where U denotes the open unit disk. We find some relationships involving functions in the class T(α,β). And we estimate the bounds of coefficients and solve Fekete-Szego problem for functions in this class. Furthermore, we investigate the bounds of initial coefficients of inverse functions or bi-univalent functions. 展开更多
关键词 Functions of Bounded positive real Part Fekete-Szego Problem Inverse Functions Bi-Univalent Functions
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A new positive real characterization and robust positive real control of descriptor systems
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作者 Hanyong SHAO Chunbo FENG 《控制理论与应用(英文版)》 EI 2005年第2期200-204,共5页
This paper investigates the positive real control problem for uncertain descriptor systems. The parametric uncertainty is assumed to be norm bounded. Firstly, for the nominal system, a new positive real characterizati... This paper investigates the positive real control problem for uncertain descriptor systems. The parametric uncertainty is assumed to be norm bounded. Firstly, for the nominal system, a new positive real characterization is given, which is expressed by a strict linear matrix mequality(LMI) without equality constraints. Secondly, for the uncertain system, necessary and sufficient conditions for the solvability of the positive real control problem are derived. Based on these conditions a state feedback law is obtained, which renders the resultant closed-loop system robustly positive real. 展开更多
关键词 Descriptor system Parameter uncertainty positive real control State feedback
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The Refined Schwarz-Pick Estimates for Positive Real Part Holomorphic Functions in Several Complex Variables
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作者 Xiaosong LIU 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2023年第2期265-278,共14页
In this article,the refined Schwarz-Pick estimates for positive real part holomorphic functions p(x)=p(0)+Σ_(m=k)^(∞)D^(M)p(0)(x^(m))/m!:G→Care given,where k is a positive integer,and G is a balanced domain in comp... In this article,the refined Schwarz-Pick estimates for positive real part holomorphic functions p(x)=p(0)+Σ_(m=k)^(∞)D^(M)p(0)(x^(m))/m!:G→Care given,where k is a positive integer,and G is a balanced domain in complex Banach spaces.In particular,the results of first order Fréchet derivative for the above functions and higher order Frechet derivatives for positive real part holomorphic functions p(x)=p(0)+Σ_(s=1)^(∞)D^(sk)p(0)(x^(sk))/(sk)!:G→Care sharp for G=B,where B is the unit ball of complex Banach spaces or the unit ball of complex Hilbert spaces.Their results reduce to the classical result in one complex variable,and generalize some known results in several complex variables. 展开更多
关键词 Refined Schwarz-Pick estimate positive real part holomorphic function First order Fr´echet derivative Higher order Fréchet derivatives
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Robust strictly positive real synthesis for polynomial families of arbitrary order
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作者 YUWensheng WANGLong JürgenAckermann 《Science in China(Series F)》 2004年第4期475-489,共15页
For any two n-th order polynomials a(s) and b(s), the Hurwitz stability of their convex combination is necessary and sufficient for the existence of a polynomial c(s) such that c(s)/a(s) and c(s)/b(s) are both strictl... For any two n-th order polynomials a(s) and b(s), the Hurwitz stability of their convex combination is necessary and sufficient for the existence of a polynomial c(s) such that c(s)/a(s) and c(s)/b(s) are both strictly positive real. 展开更多
关键词 robust stability strict positive realness robustness analysis and synthesis polynomial segment.
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FOUR WHEELS DRIVEN INDEPENDENTLY BY ONE PUMP DRIVING FOUR HYDRAULIC MOTORS 被引量:3
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作者 WuBaolin QiuLihua WangZhanlin 《Chinese Journal of Mechanical Engineering》 SCIE EI CAS CSCD 2005年第2期232-236,共5页
An improved Narendra model reference adaptive control (MRAC) scheme isproposed to research one variable displacement pump driving four hydraulic variable displacementmotors. This approach not only ensures the underdam... An improved Narendra model reference adaptive control (MRAC) scheme isproposed to research one variable displacement pump driving four hydraulic variable displacementmotors. This approach not only ensures the underdamped and unstable system be global uniformasymptotic stability, but also has good robustness in these aspects of modeling uncertainty,pressure fluctuation of constant pressure network, and disturbance from external load, which alsoupgrades the rapidity of system response so as to make controlled system with nicer dynamic quality.The scheme of one pump driving four motors can meet the demand on off-road mobility of engineeringvehicles and armored cars. A proof of stability about improved Narendra MRAC scheme is also given. 展开更多
关键词 Constant pressure network Rotational speed control Model reference adaptivecontrol(MRAC) Strict positive realness Global uniform stability
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Generalized Negative Imaginary Lemma for Descriptor Systems 被引量:2
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作者 Mohamed A. Mabrok Abhijit G. Kallapur +1 位作者 Ian R. Petersen Alexander Lanzon 《Journal of Mechanics Engineering and Automation》 2012年第1期17-21,共5页
Flexible structure dynamics with collocated force actuators and position sensors lead to negative imaginary (NI) systems. In this paper, the authors study the extension of NI theory to descriptor systems. The author... Flexible structure dynamics with collocated force actuators and position sensors lead to negative imaginary (NI) systems. In this paper, the authors study the extension of NI theory to descriptor systems. The authors derive an NI lemma for descriptor systems. This is done by using the transformation from positive real (PR) system to NI system. Then, the Weierstrass Form transformation was involved to transform A and E matrices to be in a special form. An illustrative example is presented to support the result. Negative imaginary systems, positive real systems, descriptor systems, Negative imaginary lemma. 展开更多
关键词 positive real negative imaginary descriptor systems.
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NEW SUBCLASS OF ANALYTIC FUNCTIONS IN CONICAL DOMAIN ASSOCIATED WITH A LINEAR OPERATOR
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作者 Muhammed ARIF Shahid MAHMOOD +1 位作者 Janusz SOKOL Jacek DZIOK 《Acta Mathematica Scientia》 SCIE CSCD 2016年第3期704-716,共13页
The main object of the present paper is to investigate a number of useful properties such as inclusion relations, distortion bounds, coefficient estimates, subordination results, the Fekete-Szego problem and some othe... The main object of the present paper is to investigate a number of useful properties such as inclusion relations, distortion bounds, coefficient estimates, subordination results, the Fekete-Szego problem and some other for a new subclass of analytic functions, which are defined here by means of linear operator. Relevant connections of the results presented here with those obtained in earlier works are also pointed out. 展开更多
关键词 analytie functions SUBORDINATION functions with positive real part linear operators conic domains
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Robustness analysis of control systems with disc uncertainties
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作者 Zhizhen WANG Long WANG Wensheng YU 《控制理论与应用(英文版)》 EI 2005年第4期327-333,共7页
For a class of control systems with disc uncertainties, robust performance anaysis is developed. On the strictly positive realness and H-infinity-norm of uncertain systems, from the geometric point of view, two new su... For a class of control systems with disc uncertainties, robust performance anaysis is developed. On the strictly positive realness and H-infinity-norm of uncertain systems, from the geometric point of view, two new sufficient and necessary conditions are given. The largest H-infinity-norm bound, containing the coefficients of only stable polynomials and centered at a nominal stable point in the coecient space is found. The results obtained in the paper are tractable and concise, which is illustrated by some numerical examples. 展开更多
关键词 Robusmess Disc polynomial Strictly positive realness Hurwitz stability H-infinity-norm
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Robust decentralized adaptive output feedback fuzzy controller design and application to AHS
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作者 Yishao Huang Dequn Zhou +2 位作者 Xiaoxin Chen Xueyun Chen Zhengwu Wang 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2010年第5期842-849,共8页
A novel decentralized indirect adaptive output feedback fuzzy controller is developed for a class of large-scale uncertain nonlinear systems using error filtering.By the properly filtering of the observation error dyn... A novel decentralized indirect adaptive output feedback fuzzy controller is developed for a class of large-scale uncertain nonlinear systems using error filtering.By the properly filtering of the observation error dynamics,the strictly positive-real condition is guaranteed to hold such that the proposed output feedback and adaptation mechanisms are practicable in practice owing to the fact that its implementation does not require the observation error vector itself any more,which corrects the impracticable schemes in the previous literature involved.The presented control algorithm can ensure that all the signals of the closed-loop large-scale system keep uniformly ultimately bounded and that the tracking error converges to zero asymptotically.The decentralized output feedback fuzzy controller can be applied to address the longitudinal control problem of a string of vehicles within an automated highway system(AHS) and the effectiveness of the design procedure is supported by simulation results. 展开更多
关键词 large-scale nonlinear system fuzzy control output feedback decentralized control strictly positive real(SPR) condition automated highway system(AHS).
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A Backstepping Simple Adaptive Control Application to Flexible Space Structures 被引量:4
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作者 LIU Min XU Shijie HAN Chao 《Chinese Journal of Aeronautics》 SCIE EI CSCD 2012年第3期446-452,共7页
Although the simple adaptive control (SAC) is widely studied both in theory and application in flexible space structure control and other control problems, it is restricted by the almost strictly positive real (ASP... Although the simple adaptive control (SAC) is widely studied both in theory and application in flexible space structure control and other control problems, it is restricted by the almost strictly positive real (ASPR) conditions. In most practical control problems, the ASPR conditions are not satisfied. Therefore, based on the SAC theory, this paper proposes a backstepping simple adaptive control algorithm which suits the system with arbitrary relative degree with no need of parallel feed forward compensa- tor. The proposed control algorithm consists of decomposition of the arbitrary relative degree system into a known subsystem and an unknown ASPR subsystem which are connected in cascade, design of constant output feedback controller for the known subsystem, and implementation of backstepping method and SAC of the unknown ASPR subsystem. Inheriting the characteristics of the SAC, this method can be adaptive online for the parameter uncertainties. Then, the application of the proposed controller to large flexible space structure with collocated sensors and actuators is studied, and the simulation results validate the proposed controller. It is a new strategy to apply the classical SAC to high relative degree plants. 展开更多
关键词 simple adaptive control almost strictly positive real BACKSTEPPING flexible structure intermediate control law
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Observer-based Variable Universe Adaptive Fuzzy Controller Without Additional Dynamic Order 被引量:1
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作者 Hai-Gang Guo Bao-Jie Zhang 《International Journal of Automation and computing》 EI CSCD 2014年第4期418-425,共8页
A high-precision fuzzy controller, based on a state observer, is developed for a class of nonlinear single-input-single-output(SISO) systems with system uncertainties and external disturbances. The state observer is i... A high-precision fuzzy controller, based on a state observer, is developed for a class of nonlinear single-input-single-output(SISO) systems with system uncertainties and external disturbances. The state observer is introduced to resolve the problem of the unavailability of state variables. Assisted by the observer, a variable universe fuzzy system is designed to approximate the ideal control law. Being auxiliary components, a robust control term and a state feedback control term are designed to suppress the influence of the lumped uncertainties and remove the observation error, respectively. Different from the existing results, no additional dynamic order is required for the control design. All the adaptive laws and the control law are built based on the Lyapunov synthesis approach, and the signals involved in the closed-loop system are guaranteed to be uniformly ultimately bounded. Simulation results performed on Duffing forced oscillation demonstrate the advantages of the proposed control scheme. 展开更多
关键词 Variable universe fuzzy system OBSERVER strictly positive real (SPR) condition dynamic order σ-modification adaptive bounding technique
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Retrospect and prospect on integration of gain and phase for feedback stability analysis
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作者 Di Zhao Li Qiu 《Control Theory and Technology》 EI CSCD 2022年第4期555-558,共4页
In this paper,we review existing approaches to integrating small gain and small phase analysis for feedback stability of dynamical systems,and give a brief outlook for possible future directions in exploring this topi... In this paper,we review existing approaches to integrating small gain and small phase analysis for feedback stability of dynamical systems,and give a brief outlook for possible future directions in exploring this topic.Small gain analysis has been very successful and popular in control theory since 1960s,while the small phase analysis for multiple-input-multiple-output systems has not been well understood until recently and is now gradually taking shape.Nevertheless,there have been attempts to analyzing feedback stability via the integration of gain and phase information over decades,including the combination of small gain with positive realness as well as that with negative imaginariness.Such combinations can be subsumed into a recently proposed framework for gain-phase integration,which brings in new geometrical methods and also sheds new lights on several future directions. 展开更多
关键词 Small gain Small phase PASSIVITY positive real Negative imaginary Davis-Wielandt shell
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