Showing papers by "Minyue Fu published in 1988"
TL;DR: In this article, a closed form for the maximal perturbation bounds under which stability is preserved was derived for the stability box around the coefficients of a nominally stable polynomial.
115 citations
TL;DR: In this article, counterexamples illustrate the fundamental differences between polynomial and matrix-stability problems and indicate that some obvious lines of attack on the matrix polytope stability problem will fail.
Abstract: While there have been significant breakthroughs for the stability of a polytope of polynomials since V.L. Kharitonov's (1978) seminal result on interval polynomials, for a polytope of matrices, the stability problem is considered far from completely resolved. Counterexamples are provided for three conjectures that are directly motivated by the results in the polynomial case. These counterexamples illustrate the fundamental differences between polynomial-stability and matrix-stability problems and indicate that some obvious lines of attack on the matrix polytope stability problem will fail. >
102 citations
15 Jun 1988
TL;DR: In this article, the edge criterion is extended to handle any region D whose complement Dc has the following property: every point d Dc lies on some continuous path which remains within Dc and is unbounded.
Abstract: In Bartlett, Hollot and Lin [2], a fundamental result is established on the zero locations of a family of polynomials. It is shown that the zeros of a polytope P of n-th order real polynomials is contained in a simply connected region D if and only if the zeros of all polynomial along the exposed edges of P are contained in D. This paper is motivated by the fact that the requirement of simple connectedness of D may be too restrictive in applications such as dominant pole assignment and filter design where the separation of zeros is required. In this paper, we extend the "edge criterion" in [2] to handle any region D whose complement Dc has the following property: Every point d Dc lies on some continuous path which remains within Dc and is unbounded. This requirement is typically verified by inspection and allows for a large class of disconnected regions. We also allow for polynomials with complex coefficients.
28 citations
07 Dec 1988
TL;DR: In this paper, the edge stability of a polytope of quasipolynomials was studied and a polar-plot-based graphical test was proposed to check the stability of the edges.
Abstract: The authors consider the D-stability problem for a class of uncertain delay systems where the characteristic equations involve a polytope of quasipolynomials. Their first result shows that under a mild assumption on the set D, a polytope of quasipolynomials is D-stable if and only if the edges of the polytope are D-stable. This extends the edge theorem developed by A.C. Bartlett, et. al. (1987) and M. Fu and B.R. Barmish (1988) for the D-stability of a polytope of polynomials. The second result provides a polar-plot-based graphical test for checking the D-stability of a polytope of quasipolynomials. In a special case in which the vertical quasipolynomials are in a factored form, the graphical test is further simplified by a special mapping. As shown in an example, the graphical tests provided here are quite useful in applications, making it possible to handle examples with many uncertain parameters easily. >
8 citations
TL;DR: Under some mild hypotheses, a piecewise linear time-invariant switching control law based on the reduced order models leading to a guarantee of Lyapunov stability with an exponential rate of convergence for the state is generated.
5 citations