## Search

Now showing items 1-8 of 8

#### On the Method of Vector Lyapunov Functions

(University of Texas at Arlington, 1974-09)

The method of vector Lyapunov functions consists of employing several Lyapunov-like functions and the theory of vectorial differential inequalities. This general comparison technic leads to a more flexible mechanism to ...

#### Practical Stability and Lyapunov Functions

(University of Texas at Arlington, 1979-10)

The notion of "practical stability" was discussed in the monograph by LaSalle and Lefschetz [6] in which they point out that stability investigations
may not assure "practical stability" and vice versa. For example an ...

#### On the Existence of Solutions of Differential Equations in a Banach Space

(University of Texas at Arlington, 1974-03)

The study of Cauchy problem for differential equations in a Banach space has taken two different directions. One approach is to find compactness type conditions [1,2,4,9,14] to guarantee existence of solutions only and the ...

#### Cone-Valued Lyapunov Functions

(University of Texas at Arlington, 1976-08)

It is very well known that employing a single
Lyapunov function and the theory of scalar
differential inequality offers a useful
mechanism to study a variety of qualitative
problems of differential equations ...

#### Differential Equations on Closed Subsets of a Banach Space

(University of Texas at Arlington, 1974-07)

The problem of existence of solutions to the initial value problem [see pdf for notations], where [see pdf for notations], F is a locally closed subset of a Banach space E. Nonlinear comparison functions and dissipative ...

#### Quasi-Solutions, Vector Lyapunov Functions and Monotone Method

(University of Texas at Arlington, 1980-02)

It is now well known that the method of vector Lyapunov functions provides an effective tool to investigate the properties of large scale
interconnected dynamical and control systems. [3,4,5,11-15]. Several Lyapunov ...

#### A Technique in Stability Theory of Delay-Differential Equations

(University of Texas at Arlington, 1978-04)

In the study of stability theory for delay-differential equations using Lyapunov functions and the theory of differential inequalities, it becomes necessary to choose an appropriate minimal class of functions relative to ...

#### On Perturbing Lyapunov Functions

(University of Texas at Arlington, 1974-02)

It is known [2,3] that in proving uniform boundedness of a differential system by means of Lyapunov functions, it is sufficient to impose conditions in the complement of a compact set in [see pdf for notation], whereas, ...