Static output feedback passivation revisited and global asymptotic stabilizing properties of a controller

Abstract

The class of systems that can be globally asymptotically stabilized by the well-known control law u = −y, = Γyy T is extended, in respect to literature. This control law is suitable for application to systems of unknown structure, and it is shown that it is more advantageous than the linear control law. The stability proof is based on solutions of a newly introduced problem, which is a specialization of the passivation by static output feedback control of a system with nonzero feedforward matrix. Necessary and sufficient conditions for existence of a solution of the problem are given, which include the minimum phase property of the given system. It is explained why the new concept cannot be applied to nonminimum phase systems. It is proved that a class of nonminimum phase systems can be stabilized by the same control law, where Γ is a matrix function, rather than a constant matrix. Illustrative example are given.

Robust stabilization under structured, possibly unstable and impulsive uncertainties

“…As 𝛽 i < 1, using the Schur complement and inequality (9), we obtain that inequality (10) is equivalent with…”

“…The literature on robust control is huge, here we mention only approaches: The approach of quadratic stability combined with scaling, sections III and IV.C of Reference 3, the approach of integral quadratic constraints (IQCs), see References 4,5, ‐analysis in Reference 6, (L–R iteration) and section 11 of Reference 1 (D–K iteration), BMI approach for design of locally optimal controllers in Reference 7, control of uncertain descriptor systems of polytopic type in Reference 8 (theorem 3), and the approach with SOF passivation in Reference 9. For an extensive review, see Reference 7.…”