菱形对象族的鲁棒镇定*

本文研究了菱形对象族的鲁棒镇定问题，证明了控制器鲁棒镇定菱形对象族的充分必要条件是它同同时镇定六十四条棱边对象，在此基础上，利用凸方向的概念讨论了控制器分子、分母的选择，并给出了菱形对象族的顶点镇空结果。     

多输入多输出系统在凸多面体摄动模式下H∞鲁棒性能

研究了多输入多输出混合摄动系统的加权H∞ 范数的检验问题 ,对象族的分子为多仿射凸多面体多项式族 ,当分母为乘积形式的多仿射凸多面体多项式族时 ,给出了棱边检验结果 ,当对象族的分母多项式族为区间多项式族或菱形多项式族时 ,给出了顶点检验结果     

多线性凸多面体对象族的鲁棒镇定

研究了由多个不确定对象串联所构成的多线性凸多面体对象族的鲁棒镇定问题,在对控 制器的结构进行某些假设的条件下,给出了控制器鲁棒镇定对象族的充分必要条件是它同时镇定 所有的顶点对象.     

多输入多输出系统在凸多面体摄动模式下H∝鲁棒性能

研究了多输入多输出混合摄动系统的加权Ｈ∝范数的检验问题,对象族的分子为多仿射凸多面体多项式族,当分母为乘积形式的多仿射凸多面体多项式族时,给出了棱边检验结果,当对象族的分母多项式族为区间多项式族或菱形多项式族时,给出了顶点检验结果。     

一类参数不确定性系统的鲁棒控制

讨论了带有分母多项式摄动的参数不确定性系统的鲁棒镇定问题,给出了这类参数 不确定性系统存在鲁棒控制器的一个充分条件,并且当这个条件被满足时,得到了部分鲁棒 控制器的一个参数化公式.     

鲁棒严格正实镇定的顶点结果

本文主要研究了区间系统的鲁棒严格正实镇定问题。文中首先给出了系统严格正实镇定的充分条件。然后分析了该条件的可计算性并对一类区间分母系统获得了采用一阶控制器时鲁棒严格正实镇定的顶点结果，使得控制器设计大为简化。     

鲁棒镇定区间系统族的一个充分条件

讨论了区间系统族的鲁棒镇定问题,给出存在控制器鲁棒镇定区间系统族的一个充分条 件,并且当这个条件成立时,得到了鲁棒镇定区间系统族的控制器的参数化公式.     

球形对象族的最优鲁棒镇定

本文对球形对象族系统最优鲁棒镇定问题进行了研究.利用最小范数解方法求解球形对象族的可镇定性半径.可镇定性半径是系统稳定性半径的上界,最优控制器的稳定性半径等于镇定性半径.文中给出球形对象族最优鲁棒控制器的形式,并通过示例具体说明球形对象族最优鲁棒控制器的设计方法.     

零点位于左扇区的多项式菱形族

本文考虑多项式菱形族的左扇区稳定性,证明了多项式族左扇区稳定的充分必要条件是的至多4q(q—1)条特殊棱边左扇区稳定;进一步,在一定条件下,只要检验的4q个顶点多项式就可确定的左扇区稳定性。     

同时镇定及鲁棒控制器存在条件

在保证闭环系统稳定的前提下，将被控对象看成控制器，控制器看成被控对象。从集合的角度研究了镇定区间对象族的控制器存在条件和设计方法，利用值集的概念和Youla参数化结果给出了镇定区间对象族控制器存在的充分条件．在强约束条件下，得到了控制器存在的充要条件．最后给出了鲁棒镇定控制器的设计方法．     

Extreme point results for robust stabilization of interval plantswith first-order compensators

It has been shown previously that a first-order compensator robustly stabilizes an internal plant family if and only if it stabilizes all of the extreme plants. These extreme plants are obtained by considering all possible combinations for the extreme values of the numerator and denominator coefficients. In this work, the authors prove a stronger result, namely, that it is necessary and sufficient to stabilize only sixteen of the extreme plants. These sixteen plants are generated using the Kharitonov polynomials associated with the numerator and denominator. Furthermore, when additional information about the compensator is specified (sign of the gain and signs and relative magnitudes of the pole and zero), then, in some cases, it is necessary and sufficient to stabilize eight critical plants, while, in other cases, it is necessary and sufficient to stabilize twelve critical plants     

To stabilize an interval plant family it suffices to simultaneouslystabilize sixty-four polynomials

It is shown that stability of three specific polynomial families can be deduced from the stability of a finite number of polynomials. These polynomial families are the characteristic polynomials of unity feedback loops with the controller in the forward path, and where the plant includes a specific form of parameter uncertainty. For the first polynomial family, the plant has parameter uncertainty in the even or odd terms of the numerator or denominator polynomial. For the second polynomial family the plant has a numerator or denominator which is an interval polynomial. For the third polynomial family, the plant is interval. Because of the structure of these results it is shown that they lead to robust stabilization results. Two examples are included. The approach employed here was developed for plants with affine uncertainty. It is demonstrated that considerable simplification results if the plants under investigation are interval     

On the thirty-two virtual polynomials to stabilize an intervalplant

This paper studies the conservatism of the 32 virtual polynomials to stabilize an interval plant. It is shown that working with the 32 virtual vertices is generally less conservative than with the Kharitonov polynomials of the smallest interval polynomial containing the characteristic polynomial polytope. By means of the former, it is possible to find all the controllers such that the value set of the polytope of characteristic polynomials is applied in two quadrants as a maximum for each ω; while using the latter, only some of them can be found. The cases in which both methods coincide are also analyzed, and the conditions on the numerator and denominator of the controller are developed. Thus, this coincidence can be known a priori from the characteristics of the coefficients of the numerator and denominator of the controller. It is shown that these conditions are satisfied by the first-order controllers     

Robust tracking: relation between the numerators, mode readability,and inverse internal model

In the robust, multivariable, asymptotic tracking problem with two-output plants, it is shown that if the numerator related to the controlled output is fixed, while the other numerator and the denominator are perturbed, then there is no solution to the problem. If, however, the whole part of the plant related to the controlled output is stable and fixed, while the other part is arbitrarily perturbed, the problem has a solution and the compensator that solves the problem incorporates an “inverse internal model” of the signal to be tracked     

Optimizing simultaneously over the numerator and denominator polynomials in the Youla-Kuc/spl caron/era parametrization

Traditionally, when approaching controller design with the Youla-Kuc/spl caron/era parametrization of all stabilizing controllers, the denominator of the rational parameter is fixed to a given stable polynomial, and optimization is carried out over the numerator polynomial. In this note, we revisit this design technique, allowing to optimize simultaneously over the numerator and denominator polynomials. Stability of the denominator polynomial, as well as fixed-order controller design with H/sub /spl infin// performance are ensured via the notion of a central polynomial and linear matrix inequality (LMI) conditions for polynomial positivity.     

Design of PID controllers for interval plants with time delay

First of all, the box theorem is extended to the interval plants with the fixed delay. An approach is presented to design the PID controller for interval plants with the fixed delay, which can obtain all of the stabilizing PID controllers. Then, using Hermite–Biehler theorem, extreme point results are provided by the virtual quasi-polynomials. When two virtual and two vertex quasi-polynomials corresponding to a Kharitonov-like segment plant are stable under a particular PID controller, it is sufficient that the same PID controller can stabilize this Kharitonov-like segment plant. The virtual quasi-polynomials are obtained in a simple way, and they are expressed in terms of the controller and the Kharitonov polynomials of the interval plants. A PID controller stabilizes interval plants with the fixed delay if it simultaneously stabilizes thirty-two quasi-polynomials. The example is given to illustrate the proposed method.     

Minimality, stabilizability, and strong stabilizability ofuncertain plants

This paper considers a set of uncertain transfer functions whose numerator and denominators belong to independent polytopes. It shows that i) the members of this set are free from pole-zero cancellations iff all the ratios of numerator edges and denominator edges are free from pole-zero cancellations and the numerator and denominator corners evaluated at a finite number of points satisfy certain phase conditions, ii) the members of this set are free from pole zero cancellations in the closed right half plane, iff all the ratios of numerator edges and denominator edges are free from pole-zero cancellations in the closed right half plane, and the numerator and denominator corners evaluated at a finite number of points satisfy certain phase conditions, and iii) in the strictly proper case, all plants in the set are strongly stabilizable iff all plants avoid pole-zero cancellations in the closed right half plane and all the corner ratios are strongly stabilizable. A counter-example is presented to show that this last result does not extend to biproper plants     

Controller synthesis via the 4-polynomial approach

In some recent work it was shown that to stabilize systems with real parameter uncertainty it suffices to find a controller that simultaneously stabilizes a finite number of polynomials. These polynomials include those generated from the ‘vertex’ plants as well as some generated by some ‘fictitious’ vertex plants that involve the controller. This paper deals with the issues of existence of such a controller, controller synthesis, and conservativeness of the design. It is shown how this approach can ‘enhance’ the stability robustness of an H_∞ design.