On the order of stable compensators
Automatica (Journal of IFAC)
Optimal diagonal scaling for infinity-norm optimization
Systems & Control Letters
An algorithm for interpolation with units in H∞, with applications to feedback stabilization
Automatica (Journal of IFAC)
Unit interpolation in H∞ : bounds of norm and degree of interpolants
Systems & Control Letters
Control of uncertain systems: a linear programming approach
Control of uncertain systems: a linear programming approach
Robust and optimal control
Single-loop feedback-stabilization of linear multivariable dynamical plants
Automatica (Journal of IFAC)
| Hi-index | 22.14 |
The problem of computing units in RH"~ that satisfy Ball-Gohberg-Rodman two-sided tangential interpolation conditions over the open right half complex plane is considered. We first show that every unit in RH"~ can be written (up to left multiplication by an orthogonal matrix) as a finite product of positive real functions in RH"~ with invertible value at ~. This factorization is used to recast interpolation conditions on units as coupled positive real interpolation problems for the factors. An algebraic necessary and sufficient condition for the existence of solutions and a parameterization of all solutions (when one exists) are given. We introduce a multivariable parity interlacing property for left interpolation data and present an algorithm to compute units. The algorithm involves a line search and is guaranteed to terminate in a finite number of operations when the data set has parity interlacing property. As an application, strong stabilization of LTI plants is discussed. A procedure to construct a stable stabilizing controller is given. The results are illustrated with a simple MIMO example. A necessary and sufficient condition characterizing all real rational units that satisfy tangential interpolation conditions is given. An algorithm to compute units for left interpolation is presented.