The transitivity in simultaneous stabilization

This paper deals with the transmission problem in simultaneous stabilization of time-varying linear systems. We establish two criteria for the transitivity in simultaneous stabilization. In particular, we give a necessary and sufficient condition for certain linear systems to satisfy a strengthened version of transitivity.     

Simultaneous controller design for time-varying linear systems

In this paper, we establish the parametrization of all simultaneously stabilizing controllers for two time-varying linear systems. A new approach to the simultaneous stabilization of three time-varying linear systems is also provided.     

Simultaneous stabilization with near-optimal model reference tracking

In this paper we consider the use of linear time-varying controllers for simultaneous stabilization and performance. We prove that for every finite set of plants, we can design a linear time-varying controller which provides not only closed-loop stability, but also near-optimal model reference tracking.     

基于互质因子摄动的系统非脆弱鲁棒解耦控制

研究对象和控制器存在互质因子不确定性时闭环系统鲁棒稳定和非脆弱鲁棒解耦控制问题,得到了闭环系统具有鲁棒稳定性和鲁棒解耦性能的充分条件,给出了鲁棒控制器的优化设计方法.     

Stability analysis for time-varying systems via quadratic constraints

In this paper, we introduce the concept of “quadratic constraint” (QC) to deal with various stability problems for infinite dimensional linear discrete time-varying (LTV) systems. First, we derive a necessary and sufficient condition for the close-loop stability based on quadratic constraints (QCs). An equivalent condition of this stability criterion presents the relationship between the stabilization of each finite dimensional truncation system and that of the whole system. Moreover, applying this stability criterion and the complete finiteness of the nest algebra, we show that the plant is stabilizable if and only if it has a single strong representation. Finally, we use QCs to give a necessary and sufficient condition for the robust stabilization of connected uncertainty set defined by gap metric.     

Performance bounds for coprime factor controller reductions

This paper investigates the performance of coprime factor based controller reduction methods. We show that under some mild conditions closed-loop performance bounds can be derived for observer-based controllers. The results in this paper lay a mathematical foundation for using coprime factor controller reduction methods in certain classes of controller reduction problems.     

On strong stabilization for linear time-varying systems

This paper deals with the strong stabilization problem for linear time-varying systems and gives a sufficient condition, in terms of the coprime factors, for the existence of strong stabilizers for such a system.     

Robust stabilizer design for linear time-varying internal model based output regulation and its application to an electrohydraulic system

This paper focuses on the design of a low order robust stabilizer for the tracking/disturbance rejection problem based on the internal model principle in the time-varying setting and its application to the hydraulic pressure tracking with varying frequency. The problem of this kind known as output regulation generally consists of two major parts: internal model unit construction and stabilizer design. While the construction of the time-varying internal model unit is non-trivial by itself and a very recent research outcome enables its synthesis for a class of linear time-varying systems, the effective stabilization of the augmented system (internal model unit and plant) for practical applications remains a challenge. This is due to the need to stabilize the high order time-varying augmented system using a low order stabilizer in a robust fashion and with desirable transient performance. While directly applying the stabilization approaches for a general LTV system will result in a high order stabilizer, a new method is proposed in this paper that overcomes this bottleneck by taking advantage of the unique structure of the internal model based control system. Instead of using a dynamic stabilizer with high order, this approach uses a sequence of time-varying gains that are directly injected into the internal model unit. A critical issue addressed is how to avoid the non-convex optimization associated with the time-varying gain synthesis and then convert the stabilizer design into a series of Linear Matrix Inequalities (LMIs). The proposed control approach is then demonstrated on an electrohydraulic system.     

On an open problem in bistable stabilization

We propose an equivalent representation of an open problem in bistable stabilization. Using this new formulation we derive two simple necessary condition tests for the solution of the problem. For certain special cases we also obtain the sufficient conditions.     

使用多控制器结构的可靠镇定

采用因子化方法研究了具有强镇定被控对象的可靠镇定问题.证明了几种可靠镇定问题定义之间的等价关系,并表征了可靠控制器的结构.给出了对于任意给定的控制器,存在另一个控制器使其共同解决可靠镇定问题的充要条件,该条件提供了一种选择可靠控制器的方法.     

Explicit characterization of decentralized coprime factors

This paper is concerned with parametrization of all decentralized stabilizing controllers. The auxiliary diagonal system, which is defined by the diagonal elements of Bezout factors, plays an important role in the parametrization of decentralized controllers. This paper gives an explicit characterization of the auxiliary system.     

Robustness for time-varying systems

We consider robust optimization for time-varying systems in terms of perturbations of fractional representations. Upper and lower bounds are given for the maximal radius of the operator ball around a given plant which can be stabilized by a single compensator. In the time-invariant case, these numbers are equal.