Direct state-space solution to the discrete-timeH∞ one-block problem

A general state-space representation is used to allow a complete formulation of the H_∞ optimization problem without any invertibility condition on the system matrix, unlike existing solutions. A straightforward approach is used to solve the one-block H_∞ optimization problem. The parameterization of all solutions to the discrete-time H_∞ suboptimal one-block problem is first given in transfer function form in terms of a set of functions in H _∞ that satisfy a norm bound. The parameterization of all solutions is also given as a linear fractional representation     

A computational scheme for H∞ model reduction

In this paper, a computational scheme for the H∞ model reduction problem is introduced. The scheme is illustrated by three examples. The algorithm is based on the recent characterization of the solution to the H∞ model reduction problem. A suboptimal computational procedure for the general multivariable continuous-time rth order optimal H_∞ model reduction problem is developed     

Simultaneous stabilization of MIMO systems via robustly stabilizinga central plant

In this note, a new formulation and solution to the simultaneous stabilization problem (SSP) is given. The new method is based on finding a central plant from a set of plants to be simultaneously stabilized. The theory of robust stabilization can then be applied to the central plant with a bounded perturbation, which encapsulates the plants to be stabilized, in order to solve the SSP     

H∞-norm approximation of systems by constantmatrices and related results

In this work the H_∞-norm approximation of a given stable proper rational transfer function by a constant matrix is considered. A new improved bound on H_∞-norm of a given stable transfer function is derived. Optimal approximation for relaxation systems is given     

Characterization and computation of the solution to the optimal L∞ approximation problem

The characterization of the solution to the problem of approximating a given stable, proper, rational transfer function, in L _∞ norm sense, by a rational function with prescribed number of stable and unstable modes is developed. A simple state-space suboptimal computational algorithm for the solution is presented