Singular perturbations of linear systems with multiparameters and multiple time scales

Exponential Stability of Linear Systems with Multiple Time Delays

In this paper, a class of linear systems with multiple time delays is studied. The problem of exponential stability of time-delay systems has been investigated by using Lyapunov functional method. We will convert the system of multiple time delays into a single time delay system and show that if the old system is stable then the new one is so. Then we investigate the stability of converted new ...

Singular constrained linear systems

In the linear system Ax = b the points x are sometimes constrained to lie in a given subspace S of column space of A. Drazin inverse for any singular or nonsingular matrix, exist and is unique. In this paper, the singular consistent or inconsistent constrained linear systems are introduced and the effect of Drazin inverse in solving such systems is investigated. Constrained linear system arise ...

Singular Perturbations and Time Scales in Guidance and Control of Aerospace Systems: A Survey

Systems with Multiple Time Scales

where A ( < ) is analytic in the small parameter e . Our basic result is a uniform asymptotic approximation to exp A ( e ) r that we obtain under a certain multiple semistability condition. This asymptotic approximation gives a complete multiple time scale decomposition of the above system and specifies a set of reduced order models valid at each time scale. Our contribution is threefold. 1...

singular constrained linear systems

in the linear system ax = b the points x are sometimes constrained to lie in a given subspace s of column space of a. drazin inverse for any singular or nonsingular matrix, exist and is unique. in this paper, the singular consistent or inconsistent constrained linear systems are introduced and the effect of drazin inverse in solving such systems is investigated. constrained linear system arise ...