Inertia Theorems for Operator Lyapunov Equations

Inertia theorems for operator Lyapunov inequalities

Modified Lyapunov Equations for Lti Descriptor Systems

Abstract. For linear time-invariant (LTI) state space systems it is well-known that its asymptotic stability can be related to solution properties of the Lyapunov matrix equation according to so-called inertia theorems. The question now arises how analogous results can be obtained for LTI descriptor systems (singular systems, differential-algebraic equations). The stability behaviour of a LTI d...

Some Theorems on the Inertia of General Matrices

1.1. Much is known about the distribution of the roots of algebraic equations in half-planes. (Cf. the corresponding parts in the survey [l] by Marden.) In the case of matrix equations, however, there appears to be only one known general result concerning the location of the eigenvalues of a matrix in the left half-plane. This theorem is generally known as Lyapunov’s theorem: (L,) Let A be an n...

Some New Aspect of Lyapunov Type Theorems for Stochastic Difference Equations with Continuous Time

Some new Lyapunov type theorems for stochastic difference equations with continuous time are proven. It is shown that these theorems simplify an application of Lyapunov functionals construction method.

Stability analysis of impulsive fuzzy differential equations with finite delayed state

In this paper we introduce some stability criteria for impulsive fuzzy system of differential equations with finite delay in states. Firstly, a new comparison principle for fuzzy differential system compared to crisp ordinary differential equation, based on a notion of upper quasi-monotone nondecreasing, in N dimentional state space is presented. Furthermore, in order to analyze the stability o...