Static output feedback stabilization of interconnected systems

This paper is concerned with the celebrated static output feedback control problem (SOFP) subject to linear constraints on control input KK, e.g. bounds on control magnitude, zeros in some elements of KK, etc. These constraints typically arise in the control of resource-limited systems interconnected to each other, where the local control for each system makes use of its own and neighboring systems’ outputs only, and its magnitude is bounded. This control problem can be approached by a spectral-norm minimization technique (qq-SNM), whose preliminary version was previously introduced with little mathematical justification but shown to be promising for the regular SOFP without control constraints. This paper mathematically justifies qq-SNM by showing its explicit relationship with spectral radius, and extends qq-SNM to accommodate various linear control constraints. This paper also discusses the practical application of qq-SNM to vehicle formation control, which demonstrates the merit of qq-SNM.