We present an eecient design and implementation for the solution of the Sylvester Observer matrix equation on a distributed memory computer. It consists of two main computational intensive segments, and one of a lesser complexity: the reduction of the system matrix A to a Hessenberg form, the solution of n shifted Hessenberg systems and a number of matrix-matrix multiplies. The Hessenberg reduc...

In this talk we suggest a new formula for the residual of Galerkin projection onto rational Krylov spaces applied to a Sylvester equation, and establish a relation to three different underlying extremal problems for rational functions. These extremal problems enable us to compare the size of the residual for the above method with that obtained by ADI. In addition, we may deduce several new a pr...

Sylvester equations play a central role in many areas of applied mathematics and in particular in systems and control theory. Here we will show how low-rank solutions for stable Sylvester equations can be computed based on the matrix sign function method. We discuss applications in model reduction as well as in observer design. Numerical experiments demonstrate the efficiency of the proposed me...

A novel state-space realization for parametric macromodeling is proposed in this paper. A judicious choice of the state-space realization is required to account for the generally assumed smoothness of the state-space matrices with respect to the design parameters. This is used in combination with suitable interpolation schemes to interpolate a set of state-space matrices, and hence the poles an...

We present a unifying computational framework to solve robust pole assignment problems for linear systems using state feedback. The new framework uses Sylvester equation based parametrizations of the pole assignment problems. The non-uniqueness of solutions is exploited by minimizing additionally sensitivity of closed-loop eigenvalues and the norm of the corresponding state feedback matrix. The...

By using a generalized Sylvester equation based parametrization, three minimum norm robust pole assignment problems for descriptor systems are formulated as unconstrained minimization problems for suitably chosen cost functions. The derived explicit expressions of the gradients of the cost functions allow the efficient solution of the minimization problems by using powerful gradient search base...

Abstract: A new design procedure of a reduced order unknown input observer (UIO) is proposed to generate residuals for fault detection isolation (FDI). The originality of this work consists in the adopted approach for the procedure implementation. Indeed the kernel of the actuator fault distribution matrix is generated thanks to generalized inverses. The Kronecker product is used to solve a Syl...

In this paper, we propose a new method for solving general linear systems with several right-hand sides. This method is based on global least squares method and reduces the original matrix to the lower bidiagonal form. We derive a simple recurrence formula for generating the sequence of approximate solutions {Xk}. Some theoretical properties of the new method are discussed and we also show that...

By using a Sylvester equation based parametrization, the minimum norm robust pole assignment problem for linear time-invariant systems is formulated as an unconstrained minimization problem for a suitably chosen cost function. The derived explicit expression of the gradient of the cost function allows the efficient solution of the minimization problem by using powerful gradient search based min...