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**1 - 4**of**4**### Convergence Analysis of A Parametric Robust H 2 Controller Synthesis Algorithm

"... This paper presents an iterative algorithm for solving the parametric robust H2 controller synthesis problem and analyzes the convergence properties of the algorithm on several examples. Iterative procedures are normally applied to a large class of robust control design problems in which the formula ..."

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This paper presents an iterative algorithm for solving the parametric robust H2 controller synthesis problem and analyzes the convergence properties of the algorithm on several examples. Iterative procedures are normally applied to a large class of robust control design problems in which the formulation naturally leads to bilinear matrix inequalities (BMIs). It is difficult to make concrete statements about the behavior of these iterative algorithms, except that it is often conjectured that the cost in each step of the solution procedure is reduced, which implies that the algorithms should converge to a local minimum. Similar difficulties exist for the new LMI-based iterative algorithm that we have recently proposed to solve the BMIs that occur in robust H2 control design. The effectiveness of the new algorithm has already been demonstrated on several numerical examples. This paper adds an important component to the discussion on the convergence of the new algorithm by verifying that it efficiently converges to the optimal solution. In the process, we provide some new key insights on the proposed design technique which indicate that it exhibits properties similar to the D{K iteration of the complex µ/Km-synthesis.

### LMI Synthesis of Parametric Robust H∞ Controllers

- IN PROC. AMERICAN CONTROL CONF
, 1997

"... This paper presents a new algorithm for designing full order LTI controllers for systems with real parametric uncertainty. The approach is based on the robust L2 gain analysis of the Lur'e system using Popov analysis and multipliers. The core algorithm, previously applied to the robust H2 perfo ..."

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This paper presents a new algorithm for designing full order LTI controllers for systems with real parametric uncertainty. The approach is based on the robust L2 gain analysis of the Lur'e system using Popov analysis and multipliers. The core algorithm, previously applied to the robust H2 performance synthesis problem, is shown to be applicable to the robust controller design with the H∞ cost. Although the performance metrics are different, we demonstrate that the same solution algorithm based on LMI synthesis leads to a very effective and efficient technique for real parametric robust H∞ control design. Furthermore, it is difficult to compare robust H2 controllers to =Km designs, but in this work we provide insights into the issue of conservatism for various robust H1 control approaches, in particular, the Popov controller synthesis, the robust H∞ design, and the =Km synthesis. The detailed analysis of these approaches is demonstrated on a exible structure benchmark problem.

### comfort

"... Robust finite-frequency H2 analysis of uncertain systems with application to flight comfort analysis ..."

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Robust finite-frequency H2 analysis of uncertain systems with application to flight comfort analysis

### Review A tutorial on linear and bilinear matrix inequalities

"... This is a tutorial on the mathematical theory and process control applications of linear matrix inequalities (LMIs) and bilinear matrix inequalities (BMIs). Many convex inequalities common in process control applications are shown to be LMIs. Proofs are included to familiarize the reader with the ma ..."

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This is a tutorial on the mathematical theory and process control applications of linear matrix inequalities (LMIs) and bilinear matrix inequalities (BMIs). Many convex inequalities common in process control applications are shown to be LMIs. Proofs are included to familiarize the reader with the mathematics of LMIs and BMIs. LMIs and BMIs are applied to several important process control applications including control structure selection, robust controller analysis and design, and optimal design of experiments.