Abstruct-The determination of the state-space equations of a time-varying finite-dimensional linear system with a prescribed output covariance matrix is considered when the system is excited by Gaussian whitenoise inputs. It is shown that a symmetric state covariance matrix provides the key link between the statespace equations of a system and the system output covariance matrix. Furthermore, s...

We consider weakly hyperbolic equations of the type u tt (t)+a(t)Au(t) = f(t; u(t)), u(0) = u 0 , u t (0) = u 1 ,u(t) 2 D(A), t 2 0; T], for a function u : 0; T] ?! H, T 2 0; 1], H a separable Hilbert space, A being a non-negative, self-adjoint operator with domain D(A). The real function a is assumed to be non-negative, continuous and (piecewise) continuous diierentiable, and the derivative a ...

The similarity jet of a linear scale-space is described in its most concise set of local and multi-local Euclidean invariants. The stability and (partial) equivalence of topologies on these invariants regardless additive uniform Gaussian noise is demonstrated.

An input and output model is used for the development of a model based predictive control framework for linear model structures. Diierent MPC algorithms which are based on linear state space models or linear polynomial models t into this framework. A new identiication horizon is introduced in order to represent the past.

let a be a bounded linear operator on a banach space x. we investigate the conditions of existing rank-one operator b such that i+f(a)b is invertible for every analytic function f on sigma(a). also we compare the invariant subspaces of f(a)b and b. this work is motivated by an operator method on the banach space ell^2 for solving some pdes which is extended to general operator space under some ...

In this paper, the closed form analytical expressions for the displacement field due to a cylindrical inclusion in a thermoelastic half-space are obtained. These expressions are derived in the context of steady-state uncoupled thermoelasticity using thermoelastic displacement potential functions. The thermal displacement field is generated due to differences in the coefficients of linear therma...