Singular Perturbation Approximation of Linear Hyperbolic Systems of Balance Laws

Lyapunov exponential stability of linear hyperbolic systems of balance laws

Explicit boundary dissipative conditions are given for the exponential stability in L-norm of one-dimensional linear hyperbolic sytems of balance laws ∂tξ + Λ∂xξ −Mξ = 0 over a finite space interval, when the matrix M is marginally diagonally stable. The result is illustrated with an application to boundary feedback stabilisation of open channels represented by linearised Saint-Venant-Exner equ...

Singular Perturbation Approximation for Linear Systems with Lévy Noise

To solve a stochastic linear evolution equation numerically, nite dimensional approximations are commonly used. For a good approximation, one might end up with a sequence of ordinary stochastic linear equations of high order. To reduce the high dimension for practical computations, we consider the singular perturbation approximation as a model order reduction technique in this paper. This appro...

Singular Perturbation Approximation of Balanced Systems

This paper relates the singular perturbation approximation technique for model reduction to the direct truncation technique if the system model to be reduced is stable, minimal, and internally balanced. It shows that these two methods constitute two fully compatible model reduction techniques for a continuous-time system, and both methods yield a stable, minimal, and internally balanced reduced...

A new Approach to the Multi-Objective Control of Linear Singular Perturbation Systems

Singular constrained linear systems

In the linear system Ax = b the points x are sometimes constrained to lie in a given subspace S of column space of A. Drazin inverse for any singular or nonsingular matrix, exist and is unique. In this paper, the singular consistent or inconsistent constrained linear systems are introduced and the effect of Drazin inverse in solving such systems is investigated. Constrained linear system arise ...