Inertia theorems for operator Lyapunov inequalities
نویسندگان
چکیده
منابع مشابه
Inertia Theorems for Operator Lyapunov Equations
We study operator Lyapunov equations in which the innnitesimal generator is not necessarily stable; but it satisses a spectrum decomposition assumption and it has at most nitely many unstable eigenvalues. Under mild conditions; these have unique self-adjoint solutions. We give conditions under which the number of negative eigenvalues of this solution equals the number of unstable eigenvalues of...
متن کاملStrict Stability Criteria for Impulsive Functional Differential Systems
Recommended by Alexander Domoshnitsky By using Lyapunov functions and Razumikhin techniques, the strict stability of impulsive functional differential systems is investigated. Some comparison theorems are given by virtue of differential inequalities. The corresponding theorems in the literature can be deduced from our results.
متن کاملPositive Operators and an Inertia Theorem
In recent years there has been interest in a theorem on positive definite matrices known as Lyapunov's theorem. Several authors have proved generalizations of this theorem, (WIELANDT [29J, TAUSSKY [24J, [25J, [26J , OSTROWSKISCHNEIDER [20J, GIVENS [10J, CARLSON-SCHNEIDER [3J, CARLSON [4J) . Lyapunov's theorem and its generalizations have become known as inertia theorems. In this note we shall u...
متن کاملLyapunov–type Inequalities for Third–order Linear Differential Equations
In this paper, we obtain new Lyapunov-type inequalities for the third-order linear differential equation x′′′ + q(t)x = 0 . Our work provides the sharpest results in the literature and makes corrections to those in a recently published paper [1]. Based on the above, we further establish new Lyapunov-type inequalities for more general third-order linear differential equations. Moreover, by combi...
متن کاملFurther inequalities for operator space numerical radius on 2*2 operator matrices
We present some inequalities for operator space numerical radius of $2times 2$ block matrices on the matrix space $mathcal{M}_n(X)$, when $X$ is a numerical radius operator space. These inequalities contain some upper and lower bounds for operator space numerical radius.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Systems & Control Letters
دوره 43 شماره
صفحات -
تاریخ انتشار 2001