Algorithms for constructing controllers simultaneously stabilizing second-order linear plants

We consider the simultaneous stabilization problem for second-order linear scalar stationary plants and obtain an easy-to-verify necessary condition for simultaneous stabilization as well as a sufficient condition with a constructive algorithm for designing a stabilizing controller. The problem of extending a set of simultaneously stabilizable plants is considered as well. To solve these problems, we use an approach based on the consideration of parametric spaces of polynomials and transfer functions and on a method for finding the stability radii of the 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.     

Digital Stabilizer Design for a Switched Linear Control Delay System

The problem of designing a digital controller stabilizing a continuous-time switched linear control delay system is studied. The approach to stabilization successively includes the construction of a continuous-time–discrete-time closed-loop system with a digital controller, the transition to its discrete-time model, and the construction of a discrete-time controller by simultaneous stabilization methods.     

Digital stabilizer design for a switched linear system

We consider the problem of designing a digital controller stabilizing a continuoustime switched linear system. Our approach to stabilization includes the construction of a continuous-discrete time closed-loop system, the passage to its discrete-time model, and the subsequent discrete-time controller design based on simultaneous stabilization methods.     

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．     

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.     

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.     

时变线性系统的同时稳定性

本文在算子理论框架下研究离散时变线性系统的同时稳定性.给出一个仅依赖于单边强表示的同时稳定性判据和同时镇定控制器的参数化.     

An indirect Lyapunov approach to robust stabilization for a class of linear fractional-order system with positive real uncertainty

The paper is concerned with the problem of the robust stabilization for a class of fractional order linear systems with positive real uncertainty under Riemann–Liouville (RL) derivatives. Firstly, by utilizing the continuous frequency distributed model of the fractional integrator, the fractional order system is expressed as an infinite dimensional integral order system. And via using indirect Lyapunov approach and linear matrix inequality techniques, sufficient condition for robust asymptotic stability of the fractional order systems and design methods of the state feedback controller are presented. Secondly, by using matrixs singular value decomposition technique the static output feedback controller and observer-based controller for asymptotically stabilizing the fractional order systems are derived. Finally, the validity of the proposed methods are demonstrated by numerical examples.     

Approach to simultaneous stabilization of linear dynamic plants with delay

For a finite family of continuous linear scalar stationary plants with a common constant delay in the control, we study the existence of a discrete controller simultaneously stabilizing the family with respect to the output and suggest an algorithm for constructing such a controller. The approach to the stabilization includes the construction of a continuousdiscrete (hybrid) closed system for each plant, passage to a discrete model of the system, and the subsequent finding of a common stabilizing discrete controller.     

On State Feedback Stabilization of Singular Systems with Random Abrupt Changes

This paper deals with the class of continuous-time singular linear systems with random abrupt changes. The state feedback stabilization and its robustness for this class of systems with norm-bounded uncertainties are tackled. Sufficient conditions for designing either a stabilizing controller or a robust stabilizing controller are developed in the LMI setting. The developed sufficient conditions are used to synthesize the state feedback controller that guarantees that either the nominal system or the uncertain system is piecewise regular, impulse free and stochastically stable or robust stochastically stable. The research of this author was supported by NSERC, Grant RGPIN36444-02.     

Simultaneous stabilization: Construction of a universal stabilizer for linear plants with delay with the use of spectral reducibility

We consider the problem of the construction of a common stabilizing controller for a family of k linear stationary nth-order plants with commensurable delays in the controls and the state variables. Our approach to stabilization is based on the construction of a common two-loop stabilizer. The controller of the first (internal) loop solves the problem of reducing each plant of the family to a finite spectrum, and the controller of the second (external) contour solves the stabilization problem.     

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.     

A new discrete mechanics approach to swing-up control of the cart-pendulum system

This paper develops a new swing-up control method for the cart-pendulum system via discrete mechanics. The swing-up control law consists of two parts: the swing-up stage and the stabilization one. In the swing-up stage, we use a controller based on a discrete Lyapunov function and it can swing up the pendulum. Then, in the stabilization stage, we utilize a stabilizing controller based on the linearized system and discrete-time optimal regulator theory. In addition, transformation methods from discrete control inputs into continuous zero-order hold inputs are introduced. From some simulation results, we can confirm that the cart-pendulum system is swung up and stabilized by our new method.     

一类参数不确定系统的输出反馈自适应稳定控制设计

研究一类n阶、相对阶为n-m(n为任意自然数,m≤n为非负整数)参数不确定系统的输出反馈自适应镇定控制设计问题.所给出的控制器适用于相对阶为n-m的n阶系统.通过引入一个新型的3n+2m阶动态补偿器,构造性地给出了输出反馈自适应镇定控制器的显式表达.所设计的控制器使得闭环系统所有信号有界或渐近稳定.     

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.     

Stabilizing periodic orbits of fractional order chaotic systems via linear feedback theory

In this paper stabilizing unstable periodic orbits (UPO) in a chaotic fractional order system is studied. Firstly, a technique for finding unstable periodic orbits in chaotic fractional order systems is stated. Then by applying this technique to the fractional van der Pol and fractional Duffing systems as two demonstrative examples, their unstable periodic orbits are found. After that, a method is presented for stabilization of the discovered UPOs based on the theories of stability of linear integer order and fractional order systems. Finally, based on the proposed idea a linear feedback controller is applied to the systems and simulations are done for demonstration of controller performance.     

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.     

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.     

Pole-placement controllers for linear systems with point delays

This paper presents a robust control algorithm for plants involvingboth internal (i.e. in the state) and external (i.e. in theoutput or input) known point delays. Several stabilizing controllerstructures are given and analysed for the case of perfectlymodelled plants with known parameters. The parametrized partsof two of the controller structures involve delays, while thoseof the two remaining controllers are delay-free. However, auxiliarycompensating signals which weight the plant input and outputintegrals are incorporated in all the controller structuresfor stabilization and model matching purposes.