Input/Output Stabilization in the General Two-Sided Model Matching Setup

Abstract

The problem of input-output stabilization in a general two-sided model matching setup is studied. As a first step, the problem is reduced to a pair of uncoupled bilateral Diophantine equations over RH 1. Then, recent results on bilateral Diophantine equation are exploited to obtain a numerically tractable solution given in terms of explicit state-space formulae. The resulting solvability conditions rely on two uncoupled Sylvester equations accompanied by algebraic constraints. This is in contrast to the corresponding one-sided stabilization, where no Sylvester equations are required. It is shown that imposing a mild simplifying assumption is instrumental in obtaining convenient parameterization of all stabilizing solutions, which is affine in a single RH 1 parameter. This demonstrates that if the aforementioned assumption is imposed, the general two-sided stabilization problem is similar to its one-sided counterpart in the sense that the constraints imposed by a stability requirement can be resolved without increasing problem complexity.

Feasibility and stability of preview control for 2-D discrete-time systems described by the Roesser model

“…There are not many studies that explore designing preview controllers in the frequency domain. Kristalny and Mirkin [37] have examined the issue of stability within a comprehensive twosided rational model matching framework, which has been explored in this study. The generic two-sided stability and its one-sided equivalent have different conceptual underpinnings.…”

Exosystem‐observer approach to H 2 control with output regulation constraint

“…The typical design methods of output‐regulating controllers take three types of approaches: the servocompensator approach [2, 3, 7], the Youla parameterisation approach [5, 8] and the weighting function approach [9–11]. The servocompensator approach adopted in [3, 12–14] lifts the output regulation constraint by introducing the internal models, and then considers the stabilisation of the overall systems.…”

“…The pioneering studies [12, 15] assume that the regulated output is identical to the measured output, which means that the two‐degree‐of‐freedom configurations cannot be coped with. The applicability of the weighting function approach [9–11] is also limited to the systems where the regulated output and evaluation output coincide. The more recent studies [3, 6, 14] formulate the design problems under the configuration that the regulated and measured outputs are independently defined.…”