Abstract We consider the problem of stabilizing PDE–ODE cascade systems in which input is applied to PDE system whose output drives ODE system. also dual constructing an observer for ODE–PDE system, measured. The these problems exponentially stable and unstable. While models plant both problems, actuator stabilization sensor problem. In literature, have been solved specific using backstepping a...

In this paper the output regulation of a linear distributed parameter system with a nonautonomous periodic exosystem is considered. It is shown that the solvability of the output regulation problem can be characterized by the solvability of a certain constrained infinite-dimensional Sylvester differential equation. Conditions are given for the existence of feedforward and feedback controllers s...

In this paper, Haar wavelet operational matrix method is proposed to solve a class of fractional partial differential equations. We derive the Haar wavelet operational matrix of fractional order integration. Meanwhile, the Haar wavelet operational matrix of fractional order differentiation is obtained. The operational matrix of fractional order differentiation is utilized to reduce the initial ...

Solving a system of linear equations by its normal equation usually is highly unrecommended because this approach worsens the condition number and inflates the computational cost. For linear systems whose unknowns are matrices, such as the Sylvester equation, Lyapunov equation, Stein equation, and a variate of their generalizations, the formulation of the corresponding normal equation in the se...

Many Krylov subspace methods for shifted linear systems take advantage of the invariance of the Krylov subspace under a shift of the matrix. However, exploiting this fact in the non-Hermitian case introduces restrictions; e.g., initial residuals must be collinear and this collinearity must be maintained at restart. Thus we cannot simultaneously solve shifted systems with unrelated right-hand si...