Browsing by Author "Wang, Long"
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Item Edge theorem for multivariable systems(2002-10) Wang, Long; Wang, Zhizhen; Yu, WenshengThis paper studies robustness of multivariable systems with parametric uncertainties, and establishes a multivariable version of Edge Theorem. An illustrative example is presented.Item Frequency response of uncertain systems: strong Kharitonov-like results(2002-02) Wang, LongIn this paper, we study the frequency response of uncertain systems using Kharitonov stability theory on first order complex polynomial set. For an interval transfer function, we show that the minimal real part of the frequency response at any fixed frequency is attained at some prescribed vertex transfer functions. By further geometric and algebraic analysis, we identify an index for strict positive realness of interval transfer functions. Some extensions and applications in positivity verification and robust absolute stability of feedback control systems are also presented.Item General solution to the robust strictly positive real synthesis problem for polynomial segments(2002-10) Yu, Wensheng; Wang, LongThis paper constructively solves a long standing open problem in modern control theory. Namely, 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.Item Geometric characterization of strictly positive real regions and its applications(2002-02) Wang, Long; Yu, WenshengStrict positive realness (SPR) is an important concept in absolute stability theory, adaptive control, system identification, etc. This paper characterizes the strictly positive real (SPR) regions in coefficient space and presents a robust design method for SPR transfer functions. We first introduce the concepts of SPR regions and weak SPR regions and show that the SPR region associated with a fixed polynomial is unbounded, whereas the weak SPR region is bounded. We then prove that the intersection of several weak SPR regions associated with different polynomials can not be a single point. Furthermore, we show how to construct a point in the SPR region from a point in the weak SPR region. Based on these theoretical development, we propose an algorithm for robust design of SPR transfer functions. This algorithm works well for both low order and high order polynomial families. Illustrative examples are provided to show the effectiveness of this algorithm.Item H Infinity performance of interval systems(2002-10) Wang, LongIn this paper, we study H Infinity performance of interval systems. We prove that, for an interval system, the maximal H Infinity norm of its sensitivity function is achieved at twelve (out of sixteen) Kharitonov vertices.Item Improved results on robust stability of multivariable interval control systems(2002-10) Wang, Zhizhen; Wang, Long; Yu, WenshengFor interval polynomial matrices, we identify the minimal testing set, whose stability can guarantee that of the whole uncertain set. Our results improve the conclusions given by Kamal and Dahleh.Item On the number of positive solutions to a class of integral equations(2002-02) Wang, Long; Yu, Wensheng; Zhang, LinItem Performance evaluation of switched discrete event systems(2002-02) Wang, LongThis paper discusses the asymptotic periodic behavior of a class of switched discrete event systems, and shows how to evaluate the asymptotic performance of such systems.Item A recipe for construction of the critical vertices for left-sector stability of interval polynomial(2002-02) Wang, LongFor the left-sector stability of interval polynomials, it suffices to check a subset of its vertex polynomials. This paper provides a recipe for construction of these critical vertices. Illustrative examples are presented.Item Robust D-stability of uncertain MIMO systems: LMI criteria(2002-10) Yu, Wensheng; Wang, LongThe focal point of this paper is to provide some simple and efficient criteria to judge the D-stability of two families of polynomials, i.e., an interval multilinear polynomial matrix family and a polytopic polynomial family. Taking advantage of the uncertain parameter information, we analyze these two classes of uncertain models and give some LMI conditions for the robust stability of the two families. Two examples illustrate the effectiveness of our results.Item Robust performance of a class of control systems(2002-02) Wang, LongSome Kharitonov-like robust Hurwitz stability criteria are established for a class of complex polynomial families with nonlinearly correlated perturbations. These results are extended to the polynomial matrix case and non-interval D-stability case. Applications of these results in testing of robust strict positive realness of real and complex interval transfer function families are also presented.Item Robust SPR synthesis for low-order polynomial segments and interval polynomials(2002-02) Wang, Long; Yu, WenshengWe prove that, for low-order (n 4) stable polynomial segments or interval polynomials, there always exists a fixed polynomial such that their ratio is SPR-invariant, thereby providing a rigorous proof of Anderson's claim on SPR synthesis for the fourth-order stable interval polynomials. Moreover, the relationship between SPR synthesis for low-order polynomial segments and SPR synthesis for low-order interval polynomials is also discussed.Item Robust strictly positive real synthesis for convex combination of sixth-order polynomials, Wensheng Yu and Long Wang(2002-10) Yu, Wensheng; Wang, LongFor the two sixth-order polynomials a(s) and b(s), 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. Our reasoning method is constructive, and is insightful and helpful in solving the general robust strictly positive real synthesis problem.Item Robust strictly positive real synthesis for polynomial families of arbitrary order(2002-10) Yu, Wensheng; Wang, LongFor 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.Item Stability of polytopic polynomial matrices(2002-02) Wang, Long; Wang, Zhizhen; Yu, WenshengThis paper gives a necessary and sufficient condition for robust D-stability of Polytopic Polynomial Matrices.