Related papers: Positive definiteness and stability of parametric …
This paper studies robustness of MIMO control systems with parametric uncertainties, and establishes a lower dimensional robust stability criterion. For control systems with interval transfer matrices, we identify the minimal testing set…
Typically, it is desirable to design a control system that is not only robustly stable in the presence of parametric uncertainties but also guarantees an adequate level of system performance. However, most of the existing methods need to…
In this study, the problem of robust Schur stability of $n\times n$ dimensional matrix segments by using the bialternate product of matrices is considered. It is shown that the problem can be reduced to the existence of negative eigenvalues…
It is shown that a positive linear system on a time scale with a bounded graininess is uniformly exponentially stable if and only if the characteristic polynomial of the matrix defining the system has all its coefficients positive. Then…
We investigate stability of linear delay differential systems. Stability criteria of the systems are derived based on integrals of the fundamental matrix. They are necessary and sufficient conditions for delay-dependent stability of the…
In this paper we shed more light on determinants of interval matrices. Computing the exact bounds on a determinant of an interval matrix is an NP-hard problem. Therefore, attention is first paid to approximations. NP-hardness of both…
Work of D. Stern and Bray-Kazaras-Khuri-Stern provide differential-geometric identities which relate the scalar curvature of Riemannian 3-manifolds to global invariants in terms of harmonic functions. These quantitative formulas are useful…
We consider the set Bp of parametric block correlation matrices with p blocks of various (and possibly different) sizes, whose diagonal blocks are compound symmetry (CS) correlation matrices and off-diagonal blocks are constant matrices.…
We present a novel method for checking the Hurwitz stability of a polytope of matrices. First we prove that the polytope matrix is stable if and only if two homogenous polynomials are positive on a simplex, then through a newly proposed…
The stability radius for finitely many interconnected linear exponentially stable well-posed systems with respect to static perturbations is studied. If the output space of each system is finite-dimensional, then a lower bound for the…
We prove the linear stability with respect to the Einstein-Hilbert action of the symmetric spaces $\mathrm{SU}(n)$, $n\geq3$, and $E_6/F_4$. Combined with earlier results, this resolves the stability problem for irreducible symmetric spaces…
Fourier matrices naturally appear in many applications and their stability is closely tied to performance guarantees of algorithms. The starting point of this article is a result that characterizes properties of an exponential system on a…
Linear Hamiltonian systems with time-dependent coefficients are of importance to nonlinear Hamiltonian systems, accelerator physics, plasma physics, and quantum physics. It is shown that the solution map of a linear Hamiltonian system with…
We provide convex necessary and sufficient conditions for the robust stability of linear positively dominated systems. In particular we show that the structured singular value is always equal to its convex upper bound for nonnegative…
Metzler matrices play a crucial role in positive linear dynamical systems. Finding the closest stable Metzler matrix to an unstable one (and vice versa) is an important issue with many applications. The stability considered here is in the…
We propose a numerical method, based on the shift-and-invert power iteration, that answers whether a symmetric matrix is positive definite ("yes") or not ("no"). Our method uses randomization. But, it returns the correct answer with high…
We extend the definition of $n$-dimensional difference equations to complex order $\alpha\in \mathbb{C} $. We investigate the stability of linear systems defined by an $n$-dimensional matrix $A$ and derive conditions for the stability of…
Following Cao-Hamilton-Ilmanen, in this paper we study the linear stability of Perelman's $\nu$-entropy on Einstein manifolds with positive Ricci curvature. We observe the equivalence between the linear stability restricted to the…
This paper aims at extending the criterion that the quasi-stability of a polynomial is equivalent to the total nonnegativity of its Hurwitz matrix. We give a complete description of functions generating doubly infinite series with totally…
We survey the numerical stability of some fast algorithms for solving systems of linear equations and linear least squares problems with a low displacement-rank structure. For example, the matrices involved may be Toeplitz or Hankel. We…