A new model for the interaction between the acoustic wave in an enclosed air cavity and the transversal motion of a flexible beam is proposed in this paper. This new boundary condition for the coupled wave and Euler-Bernoulli beam equations introduces sufficient damping of the energy of the system to gain uniform exponential stability. Careful physical justification of the boundary condition is...

For nonlinear systems that satisfy certain regularity conditions it is shown that upper and lower bounds on the performance (cost function) can be computed using linear or quadratic programming. The performance conditions derived from Hamilton-Jacobi inequalities are formulated as linear inequalities de ned pointwise by discretizing the state-space when assuming a linearly parameterized class o...

Constrained diffusions in convex polyhedral domains with a general oblique reflection field, and with a diffusion coefficient scaled by a small parameter ε > 0, are considered. Using an interior Dirichlet heat kernel lower bound estimate for second order elliptic operators in bounded domains from [13], certain uniform in ε lower bounds on transition densities of such constrained diffusions are ...

Global exponential stability is a desirable property for dynamic systems. This paper studies the global exponential stability of several existing recurrent neural networks for solving linear programming problems, convex programming problems with interval constraints, convex programming problems with nonlinear constraints, and monotone variational inequalities. In contrast to the existing result...

The convergence properties of adaptive systems in terms of excitation conditions on the regressor vector are well known. With persistent excitation of the regressor vector in model reference adaptive control the state error and the adaptation error are globally exponentially stable, or equivalently, exponentially stable in the large. When the excitation condition however is imposed on the refer...

The main purpose of this paper is to establish some new results onthe superstability and stability via a fixed point approach forthe Pexiderized exponential equation, i.e.,$$|f(x+y)-g(x)h(y)|leq psi(x,y),$$where $f$, $g$ and $h$ are three functions from an arbitrarycommutative semigroup $S$ to an arbitrary unitary complex Banachalgebra and also $psi: S^{2}rightarrow [0,infty)$ is afunction. Fur...