In this paper, by using majorization inequalities, upper bounds on summations of eigenvalues (including the trace) of the solution for the Lyapunov matrix differential equation are obtained. In the limiting cases, the results reduce to bounds of the algebraic Lyapunov matrix equation. The effectiveness of the results are illustrated by numerical examples.

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...

In this paper we consider various regularity results for discrete quasiperiodic Schrödinger equations −ψn+1 − ψn−1 + V (θ + nω)ψn = Eψn with analytic potential V . We prove that on intervals of positivity for the Lyapunov exponent the integrated density of states is Hölder continuous in the energy provided ω has a typical continued fraction expansion. The proof is based on certain sharp large d...

This paper concentrates on the study of adaptive control for synchronization fractional-order neural networks. Instead classical updating method, an intermittent-active strategy is proposed to adaptively tune gain in a fashion. Moreover, quantization brought into design take account restricted bandwidth signal transmission. Note that suggested controller basic yet effective terms system. The ma...

In this paper, we consider a p-Laplacian eigenvalue boundary value problem involving both right Caputo and left Riemann-Liouville types fractional derivatives. To prove the existence of solutions, apply Schaefer’s fixed point theorem. Furthermore, present Lyapunov inequality for corresponding problem.

We introduce a new algorithm to check the local stability and compute the region of attraction of isolated equilibria of nonlinear systems with polynomial vector fields. First, we consider an arbitrary convex polytope that contains the equilibrium in its interior. Then, we decompose the polytope into several convex sub-polytopes with a common vertex at the equilibrium. Then, by using Handelman’...

This paper presents a stable new algorithm for force/position control in robot manipulators. In this algorithm, position vectors are measured by sensors and then used in the control law. Since using force sensor has some issues such as high costs and technical problems, an approach is presented to overcome these issues. In this respect, force sensor is replaced by an adaptive fuzzy estimator to...

In this paper, we study one-dimensional Newtonian filtration equation including unbounded sources with multiple delays. The existence of nonnegative non-trivial time periodic solutions will be established by the Leray-Schauder fixed point theorem based on some suitable Lyapunov functionals and some a priori estimates for all possible periodic solutions.