Feedback Stabilization over Commutative Rings with no Right-/Left-Coprime Factorizations

On Robustness in the Gap Metric and Coprime Factor Uncertainty for LTV Systems

In this paper, we study the problem of robust stabilization for linear time-varying (LTV) systems subject to time-varying normalized coprime factor uncertainty. Operator theoretic results which generalize similar results known to hold for linear time-invariant (infinite-dimensional) systems are developed. In particular, we compute an upper bound for the maximal achievable stability margin under TV normalized coprime factor uncertainty in terms of the norm of an operator with a time-varying Hankel structure. We point to a necessary and sufficient condition which guarantees compactness of the TV…

Convergence of Coprime Factor Perturbations for Robust Stabilization of Oseen Systems

Linearization based controllers for incompressible flows have been proven to work in theory and in simulations. To realize such a controller numerically, the infinite dimensional system has to be linearized and discretized. The unavoidable consistency errors add a small but critical uncertainty to the controller model which will likely make it fail, especially when an observer is involved. Standard robust controller designs can compensate small uncertainties if they can be qualified as a coprime factor perturbation of the plant. We show that for the linearized Navier-Stokes equations, a linear…

A Parameterization of Stabilizing Controllers over Commutative Rings

We present a parameterization of the stabilizing controllers over commutative rings. In the classical case, that is, in the case where there exist the right-/left-coprime factorizations of the given plant, the stabilizing controllers can be parameterized by the method called ``Youla-Kucera-parameterization''. However, it is known that there exist models in which some stabilizable transfer matrices do not have their right-/left-coprime factorizations. In such models, we cannot employ the Youla-Kucera-parameterization directly. Our method of this paper can be applied to even such models.

仿射互质因子段上的精确判定与满射稳定化图册

Exact Decision and a Surjective Stabilizer Atlas for Affine Coprime-Factor Segments

针对仿射互质因子段，提出基于双Cayley分解和量词消去的精确存在性判定，并构造所有公共镇定器的满射图册。

Feedback Stabilization over Commutative Rings: Further study of the coordinate-free approach

This paper is concerned with the coordinate-free approach to control systems. The coordinate-free approach is a factorization approach but does not require the coprime factorizations of the plant. We present two criteria for feedback stabilizability for MIMO systems in which transfer functions belong to the total rings of fractions of commutative rings. Both of them are generalizations of Sule's results in [SIAM J. Control Optim., 32-6, 1675-1695(1994)]. The first criterion is expressed in terms of modules generated from a causal plant and does not require the plant to be strictly causal. It s…

有界扰动与互质因子摄动下最小相位SISO对象的自适应最优$\ell_\infty$诱导鲁棒镇定

Adaptive optimal $\ell_\infty$-induced robust stabilization of minimum phase SISO plant under bounded disturbance and coprime factor perturbations

针对有界扰动与互质因子摄动下离散最小相位SISO对象的最优鲁棒镇定问题，提出基于集员估计与参数非线性变换转化为线性分式规划的自适应控制方法，可在参数未知时以指定精度实现与已知参数对象相当的最优输出渐近上界，还支持估计与先验假设的在线验证。