An Input-Output Parametrization of Stabilizing Controllers: amidst Youla and System Level Synthesis
For control theorists and practitioners, this work simplifies the design of stabilizing controllers by eliminating pre-computation steps, but it is incremental as it builds on existing Youla and system-level synthesis frameworks.
This paper introduces a novel input-output parametrization of stabilizing controllers for LTI systems that bypasses the need for doubly-coprime factorization or an initial stabilizing controller, enabling direct computation via linear programming. It also shows that norm-optimal controllers under quadratically invariant constraints can be computed using convex programming.
This paper proposes a novel input-output parametrization of the set of internally stabilizing output-feedback controllers for linear time-invariant (LTI) systems. Our underlying idea is to directly treat the closed-loop transfer matrices from disturbances to input and output signals as design parameters and exploit their affine relationships. This input-output perspective is particularly effective when a doubly-coprime factorization is difficult to compute, or an initial stabilizing controller is challenging to find; most previous work requires one of these pre-computation steps. Instead, our approach can bypass such pre-computations, in the sense that a stabilizing controller is computed by directly solving a linear program (LP). Furthermore, we show that the proposed input-output parametrization allows for computing norm-optimal controllers subject to quadratically invariant (QI) constraints using convex programming.