Simultaneous stabilization of linear plants by a low order controller

We consider simultaneous stabilization of linear scalar stationary plants of second order and derive an easily verified necessary condition of simultaneous stabilization, as well as a sufficient condition that leads to a constructive algorithm for a stabilizing controller. The existence of a stabilizing controller is established in the parametric polynomial space by a method that finds the stability radii of polynomials.     

On some approaches to the simultaneous stabilization of linear plants by a controller of a given structure

In the present paper, we consider the problem of simultaneous stabilization of linear scalar stationary plants of arbitrary order for which we obtain numerically verifiable necessary conditions for simultaneous stabilization and a sufficient condition with the indication of a constructive algorithm for synthesizing a stabilizing controller. We also consider the problem of extending the set of simultaneously stabilized plants. For the solution of these problems, we use an approach based on the analysis of the structure of stability domains in the spaces of coefficients of polynomials linearly depending on parameters.     

A remark on the simultaneous <Emphasis Type="Italic">α</Emphasis>-stabilization of linear plants

In the present paper, we consider the problem of simultaneous α-stabilization (i.e., stabilization with degree of stability exceeding a given number α > 0) for linear scalar stationary plants of arbitrary order, for which we obtain numerically verifiable necessary conditions for simultaneous α-stabilization and a sufficient condition together with a constructive algorithm for the stabilizing controller design. To solve these problems, we use an approach based on a one-to-one transformation of the α-stability domains in the spaces of coefficients of polynomials.     

一组系统的同时稳定化

本文利用Youla参数化方法研究了多于3个系统的一组线性时变系统的同时稳定化问题,给出了这样系统稳定的一个充要条件.     

纯量反馈系统同时强镇定的充分条件

一个稳定的补偿器可同时镇定n个对象(同时强镇定)等价于一个补偿器(不一定稳定)同时镇定n 1个对象(同时镇定)．两个以上对象的同时强镇定和三个以上对象的伺时镇定是线性系统中一个急待解决的公开问题．文中所作的基本假定是所有的对象具有相同的简单不稳定零点，在此条件下给出了n个对象同时强镇定的一个充分条件．当仅有一个不稳定零点时．容易检验是否同时强镇定，否则仅需确定n个对象的不稳定零点并且判定由不稳定零点导出一个相应矩阵是正定的，就能判定n个对象同时强镇定．因此是一个易于检验的充分条件．文章同时给出了n个对象同时强镇定的算法，丰富了同时强镇定的充分条件．     

时变系统的稳定化

This paper deals with the stabilization problem for linear time-varying systems within the framework of nest algebras. We give a necessary and sufficient condition for a class of plants to be stabilizable, and we also study the simultaneous and strong stabilization problems.     

An obstruction to the simultaneous stabilization of two n-D plants

This paper calculates an obstruction to the simultaneous stabilization of twon-D plants. This obstruction is topological and lies in the (singular) cohomology of a subset of ⁿ that arises naturally in the problem. Given any family ofn-D plants, the vanishing of the corresponding cohomology classes of every pair of plants in the family is thus a necessary condition for the simultaneous stabilization of the family.     

Simultaneous stabilization of plants of various orders

We consider the problem of constructing a common controller stabilizing a finite family of linear dynamic plants of various orders with respect to state. For the solution, we use the method of extension of dynamic order, which permits one to reduce the original problem to a problem of simultaneous stabilization of plants of the same order. We state conditions for the existence of a universal stabilizer for a given finite family of dynamic plants.     

Simultaneous observability and stabilization of some uncoupled wave equations

We consider uncoupled wave equations with different speed of propagation in a bounded domain. Using a combination of the Bardos–Lebeau–Rauch observability result for a single wave equation and a new unique continuation result for uncoupled wave equations, we prove an observability estimate for that system. Applying Lions? Hilbert uniqueness method (HUM), one may derive simultaneous exact controllability results for the uncoupled system; the controls being locally distributed, with their supports satisfying the geometric control condition of Bardos, Lebeau and Rauch. Afterwards, we discuss the related simultaneous stabilization problem; this latter problem is solved by a combination of the new observability inequality, and a result of Haraux establishing an equivalence between observability and stabilization for second order evolution equations with bounded damping operators. Our observability and stabilization results generalize to higher space dimensions some earlier results of Haraux established in the one-dimensional setting.     

A unified approach to methods for the simultaneous computation of all zeros of generalized polynomials

Summary Applying Newton's method to a particular system of nonlinear equations we derive methods for the simultaneous computation of all zeros of generalized polynomials. These generalized polynomials are from a function space satisfying a condition similar to Haar's condition. By this approach we bring together recent methods for trigonometric and exponential polynomials and a well-known method for ordinary polynomials. The quadratic convergence of these methods is an immediate consequence of our approach and needs not to be proved explicitly. Moreover, our approach yields new interesting methods for ordinary, trigonometric and exponential polynomials and methods for other functions occuring in approximation theory.     

Multiple Orthogonal Polynomials on the Unit Circle

We introduce multiple orthogonal polynomials on the unit circle. We show how this is related to simultaneous rational approximation to Caratheodory functions (two-point Hermite-Pade approximation near zero and near infinity). We give a Riemann-Hilbert problem for which the solution is in terms of type I and type II multiple orthogonal polynomials on the unit circle, and recurrence relations are obtained from this Riemann-Hilbert problem. Some examples are given to give an idea of the behavior of the zeros of type II multiple orthogonal polynomials.     

Properties of a generalized Sylvester matrix

We consider problems close to that of the minimal stabilization of a linear vector (i.e., MISO or SIMO) dynamic system; more specifically, the problem of determining the number of common roots of a family of polynomials, and investigating the properties of the so-called generalized Sylvester matrix. The classical definition of the Sylvester matrix is valid for two polynomials, and there are different methods for defining the generalized (extended) Sylvester matrix for a family of polynomials. In this work, we consider a definition of the generalized Sylvester matrix and its properties in the context of their potential future application for solving the minimal stabilization problem.     

Stabilization of multiple-input switched linear systems by a variable-structure controller

We consider the stabilization problem for multiple-input switched linear systems operating under bounded coordinate disturbances and arbitrary switching signals. To solve this problem, we suggest an algorithm for the construction of a variable-structure controller based on methods of simultaneous stabilization theory.     

Stabilization of switched linear systems by a controller of variable structure

We study the state stabilization problem for switched linear systems operating under parametric uncertainty and bounded coordinate disturbances. To solve the problem, we suggest an algorithmfor constructing a controller of variable structure on the basis of methods of simultaneous stabilization theory.     

Global stabilization of a certain class of nonlinear dynamical systems using state detection

This note is concerned with the stabilization of control systems using an estimated state feedback. The global stabilization problem for a relatively broad class of nonlinear plants is discussed. Moreover, using the “input to state stability” property introduced by Sontag [1–4] and detectability condition, we show that the system can be globally asymptotically stable using a state detection.     

Robust stabilization of multilinear interval plants by Takagi–Sugeno fuzzy controllers

This study investigates the stabilization problem of interval and multilinear interval plants. For this purpose, a Takagi–Sugeno fuzzy state model, expressed in the form of an interval system, is considered as a robust stabilizing controller for the plants with interval and multilinear interval models. Based on the Zero Exclusion Condition, sufficient conditions that ensure robust stability of the presented fuzzy controller are derived as well. A two-mass-spring-damper system with multilinear uncertain parameters is studied to demonstrate the application and the effectiveness of the design process.     

Generalizations of the Hermite–Biehler theorem: the complex case

The Hermite–Biehler theorem gives necessary and sufficient conditions for the Hurwitz stability of a polynomial in terms of certain interlacing conditions. In this paper, we extend our earlier generalization of the Hermite–Biehler theorem for real, not necessarily Hurwitz polynomials to the domain of polynomials with complex coefficients. This result, which is of interest in its own right, can also be used to analytically solve an important stabilization problem in control theory.     

复赋范空间中复RS集的最佳同时逼近

研究了复赋范空间中具限制系数的广义多项式集G对无穷序列的最佳同时逼近问题,得到了特征定理;当G是复RS集时还得到了惟一性定理．     

Error analysis of signal zeros from a related companion matrix eigenvalue problem

An error analysis of the so-called signal zeros of polynomials linked to exponentially damped signals is performed and error bounds are derived. The analysis uses the link between polynomials and companion matrices and allows us to show that the related companion matrix eigenvalue problem is governed by the condition number of a rectangular Vandermonde matrix which has the zeros of interest as nodes. Conditions under which the zeros are well conditioned are discussed.     

Banach algebra methods in prediction theory

In a series of papers, Baxter has exploited with great success an equivalence between Szegö polynomials orthogonal on the unit disc, and a certain difference system satisfied by polynomials closely related to the Szegö polynomials. The polynomials occuring in Baxters difference system turn up, as is well known, in a problem of prediction. The present paper follows closely the ideas of Baxter. Apart from some generalizations, the novelty lies in an improved technique.