Abstract
In this paper the asymptotic stability is concerned for a class of neutral delay differential-algebraic equations (NDDAEs). We will present two criteria by evaluating a corresponding harmonic function on the boundary of a torus region. Stability regions are also presented so as to locate all possible unstable characteristic roots of NDDAEs. As we know, these roots will make bad numerical simulations. Our criteria help find and avoid them. Numerical examples are shown to check our criteria.
Highlights
Functional differential equations (FDEs) have a wide range of applications in science and engineering
Among them, retarded and neutral FDEs have more applications in real world problems. They appear in the form of delay differential equations (DDEs) and neutral delay differential equations (NDDEs) [1,2,3,4,5,6]
It is known that analytical solutions of these equations can be obtained in very restricted cases, numerical methods have been wide spread for the approximation of the equations
Summary
Functional differential equations (FDEs) have a wide range of applications in science and engineering. Under the assumption of analytical stability of the system, numerical methods are discussed This assumption involves finding characteristic roots of a matrix pencil which may be numerically infeasible. Numerical computing of the roots has been discussed Note that this is a system of delay differential equations, or DDEs, and the coefficient matrix of x (t) is assumed nonsingular. The method cannot be used for delay differential-algebraic equations with a singular coefficient matrix of x (t). We are concerned with a class of generalized neutral delay differentialalgebraic equations, Kx + Lx + Mx (tτ ) + Nx(tτ ) = 0, where K, L, M, N ∈ Rd×d are constant coefficient matrices, K is singular, x(tτ ) = (x1(t – τ1), x2(t – τ2), .
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