Premium
A new static output feedback approach to the suboptimal mixed H 2 / H ∞ problem
Author(s) -
Yu Jente
Publication year - 2004
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.930
Subject(s) - initialization , control theory (sociology) , output feedback , riccati equation , equivalence (formal languages) , mathematics , iterative method , norm (philosophy) , computer science , mathematical optimization , control (management) , differential equation , mathematical analysis , discrete mathematics , artificial intelligence , political science , law , programming language
In this paper we propose a new approach to solve the static output feedback suboptimal mixed H 2 / H ∞ control problem using a state fixed‐structure feedback design. We formulate the static output feedback problem as a constrained static state feedback problem and obtain three coupled design equations: one Riccati equation, one Lyapunov equation, and a gain equation. We will prove the equivalence of the proposed solution to the existing solution. A very simple iterative algorithm is then presented to solve the design equations for the stabilizing output feedback gain that minimizes an upper bound of H 2 norm while satisfying the H ∞ disturbance attenuation requirement. A unique feature of the new approach is that it admits the Kalman gain as an initial stabilizing gain to start the above iterative solution procedure, which is computationally attractive and advantageous compared to the direct approach, as the latter has to deal with the difficult algorithm initialization problem. Some illustrative numerical examples are given to demonstrate the effectiveness of the approach. Copyright © 2004 John Wiley & Sons, Ltd.