Static output feedback: a survey

Abstract

This paper reviews the static output feedback problem in the control of linear, time-invariant (LTI) systems. It includes analytical and computational methods and presents in a unified fashion, the knowledge gained in the decades of research into this most important problem.

Hankel/Toeplitz matrices and the static output feedback stabilization problem

“…This system satisfies the PIP [28], i.e., the property that guarantees the existence of a stable stabilizer, and satisfies also the Extended PIP [28], i.e., the property that guarantees the existence of a stable stabilizer with a stable inverse. Therefore, both the PIP and the EPIP do not give an obstruction to the solvability of the SOF stabilization problem.…”

“…Many attempts have been made in the last years, so that at this stage we can count several nontrivial contributions to the problem, both numerical and speculative (see the survey paper [28] where the state of the art is presented and the existing methods are surveyed and compared).…”

Hard Problems in Linear Control Theory: Possible Approaches to Solution

“…An overview of the results in this subject area is given in [15]; for the most recent progress see [16]. Generic NP -hardness of the problem was proved in [8].…”

Synthesis of Covariance Controllers on the Basis of the System Embedding Technology

“…Primarily, this is the stability related to the properties of the Liapunov equation. The theory of covariance control can be used as one of the approaches to the synthesis of stabilizing controllers of the prescribed structure [6]. Moreover, there exists an interrelation between the robustness of a system and small deviations of the nondiagonal elements of a covariance matrix [7].…”

“…A problem for providing the prescribed state covariance matrix is solved in [6] with the aid of static controllers. In [9], these results are extended to the case of dynamic controllers of a low order (which does not exceed the order of an object).…”