This paper presents an iterative penalty function method for solving rank-constrained linear matrix inequality (LMI) problems and illustrates its application to reduced-order output feedback stabilization. We propose a penalized objective function to replace the rank condition, so that a solution to the original nonconvex LMI feasibility problem can be obtained by solving a series of convex LMI optimization subproblems. Numerical experiments were performed to demonstrate the proposed method.Index Terms-Linear matrix inequality (LMI), penalty function method, rank condition, reduced-order output feedback.
This paper presents a linear matrix inequality (LMI) approach to the design of a static output feedback controller that simultaneously stabilizes a finite collection of linear time-invariant systems. The problem is formulated as a novel rank-constrained LMI feasibility problem with a nonconvex rank condition, and is solved using an iterative penalty function method. Numerical experiments are performed to illustrate the proposed method.
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