This research introduces a row compression and nested product decomposition of an n × n hierarchical representation of a rank structured matrix A, which extends the compression and nested product decomposition of a quasiseparable matrix. The hierarchical parameter extraction algorithm of a quasiseparable matrix is efficient, requiring only O(nlog(n)) operations, and is proven backward stable. T...

For partitions of f1; : : : ; ng, the classes of P -matrices are de ned, unifying the classes of the real P -matrices and of the real positive de nite matrices. Lyapunov scalar stability of matrices is de ned and characterized, and it is shown also that every real Lyapunov -scalar stable matrix is a P -matrix. Implication relations between Lyapunov scalar stability and H-stability are discussed.

This paper presents a unified approach to formulating stability conditions for slowly time-varying linear systems and switched linear systems. The concept of total variation of a matrix-valued function is introduced to characterize the variation of the system matrix. Using this concept, a result generalizing existing stability conditions for slowly time-varying linear systems is derived. As spe...

Based on the Lyapunov–Krasovskii functionals combined with linear matrix inequality approach, a novel stability criterion is proposed for asymptotic stability of bidirectional associative memory neural networks with time delays. A novel delay-dependent stability criterion is given in terms of linear matrix inequalities, which can be solved easily by various optimization algorithms.  2005 Publi...

Abstract—This paper investigates the robust stability of uncertain neutral system with time-varying delay. By using Lyapunov method and linear matrix inequality technology, new delay-dependent stability criteria are obtained and formulated in terms of linear matrix inequalities (LMIs), which can be easy to check the robust stability of the considered systems. Numerical examples are given to ind...

This paper focuses on the problem of robust control for Takagi–Sugeno (T–S) fuzzy systemswith time-delay. The delay-dependent stability analysis and controller synthesis have been addressed. The free weighting matrix method has been used for stability analysis and controller synthesis. New and less conservative delay-dependent stability conditions are proposed in terms of linear matrix inequali...

The Schur method for computing a matrix square root reduces the matrix to the Schur triangular form and then computes a square root of the triangular matrix. We show that by using either standard blocking or recursive blocking the computation of the square root of the triangular matrix can be made rich in matrix multiplication. Numerical experiments making appropriate use of level 3 BLAS show s...

This paper introduces the notion of Lipschitz stability for nonlinear th order 8 matrix Lyapunov differential systems and gives sufficient conditions for Lipschitz stability. We develop variation of parameters formula for the solution of the nonhomogeneous nonlinear th order matrix Lyapunov differential system. We 8 study observability and controllability of a special system of th order nonline...

In this paper Kharitonov's theorem for the robust stability of interval polynomials is proved using the second method of Lyapunov. The Hermite matrix is taken as the matrix of the quadratic form which is used as a Lyapunov function to prove Hurwitz stability. I t is shown that if the four Hermite matrices corresponding to the four Kharitonov extreme polynomials are positive definite, the Hermit...

* Correspondence: [email protected] College of Science, Yanshan University, Qinhuangdao Hebei 066004, P. R. China Abstract This article deals with the problem of stability of descriptor neutral systems with multiple delays. Using Lyapunov functional and free-weighting matrix method, a delay-dependent stability criterion is obtained and formulated in the form of linear matrix inequalities, wh...