Convex Polyhedron Method to Stability of Continuous Systems with Two Additive Time-Varying Delay Components

This paper is concerned with delay-dependent stability for continuous systems with two additive time-varying delay components. By constructing a new class of Lyapunov functional and using a new convex polyhedron method, a new delay-dependent stability criterion is derived in terms of linear matrix inequalities. The obtained stability criterion is less conservative than some existing ones. Finally, numerical examples are given to illustrate the effectiveness of the proposed method

Delay-dependent stabilization of stochastic interval delay systems with nonlinear disturbances

This is the post print version of the article. The official published version can be obtained from the link below - Copyright 2007 Elsevier Ltd.In this paper, a delay-dependent approach is developed to deal with the robust stabilization problem for a class of stochastic time-delay interval systems with nonlinear disturbances. The system matrices are assumed to be uncertain within given intervals, the time delays appear in both the system states and the nonlinear disturbances, and the stochastic perturbation is in the form of a Brownian motion. The purpose of the addressed stochastic stabilization problem is to design a memoryless state feedback controller such that, for all admissible interval uncertainties and nonlinear disturbances, the closed-loop system is asymptotically stable in the mean square, where the stability criteria are dependent on the length of the time delay and therefore less conservative. By using Itô's differential formula and the Lyapunov stability theory, sufficient conditions are first derived for ensuring the stability of the stochastic interval delay systems. Then, the controller gain is characterized in terms of the solution to a delay-dependent linear matrix inequality (LMI), which can be easily solved by using available software packages. A numerical example is exploited to demonstrate the effectiveness of the proposed design procedure.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the Nuffield Foundation of the UK under Grant NAL/00630/G, and the Alexander von Humboldt Foundation of Germany

Partial Pole Placement in LMI Region

A new approach for pole placement of single-input system is proposed in this paper. Noncritical closed loop poles can be placed arbitrarily in a specified convex region when dominant poles are fixed in anticipant locations. The convex region is expressed in the form of linear matrix inequality (LMI), with which the partial pole placement problem can be solved via convex optimization tools. The validity and applicability of this approach are illustrated by two examples

Métodos lineares-quadráticos para sistemas intervalares : aplicações em controle amostrado

Orientador: Matheus SouzaDissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de ComputaçãoResumo: Robustez é uma das muitas propriedades que um sistema de controle deve apresentar, juntamente com desempenho. Neste trabalho, o objetivo é controlar um sistema linear com incertezas intervalares usando um sinal de controle amostrado a fim de minimizar um critério de desempenho quadrático. Como o desempenho depende dos parâmetros incertos do sistema, buscamos minimizar um limitante superior para o custo. Para alcançar esse objetivo, adaptamos resultados clássicos existentes na literatura para lidar com este problema de controle robusto. Os principais resultados alcançados nesta dissertação são condições de análise e de projeto de controladores robustos para sistemas intervalares baseadas em desigualdades matriciais lineares (LMIs). Estas condições consideram critérios de desempenho clássicos e foram desenvolvidas para sistemas a tempo contínuo e a tempo discreto, além de sistemas de controle amostrado. As condições desenvolvidas permanecem válidas mesmo para sistemas com incertezas variantes no tempo. Embora nossas condições sejam mais conservadoras quando comparadas à abordagem politópica, precisam apenas de um número constante de restrições e um número polinomial de variáveis de decisão, o que permite resolvê-las de modo mais eficiente mesmo para sistemas grandes ou com muitas entradas incertas. Por fim, apresentamos exemplos numéricos para apontar as principais características dos métodos propostosAbstract: Robustness is one of many properties that a control system should present, together with performance. In this thesis, we aim to control a linear system with interval uncertainties using a sampled control signal in order to minimize a quadratic performance criterion. As the performance depends on the uncertain parameters of the system, we consider minimizing a higher limit for the cost. To achieve this goal, we adapt classical results in the literature to deal with this robust control problem. The main results obtained in this thesis are robust control analysis and design conditions for interval systems based on linear matrix inequalities (LMIs). These conditions consider classic performance indices and were developed for continuous and discrete-time systems, as well as sampled-data systems. The devised conditions remain valid even for time-varying uncertain systems. Although our conditions are more conservative when compared with the polytopic approach, they need only a constant number of constraints and a polynomial number of variables, which allows them to be solved more efficiently even for large systems with many uncertain inputs. Finally, we present numerical examples to point out the main characteristics of the proposed methodsMestradoAutomaçãoMestre em Engenharia ElétricaCAPE

Comments on "Quadratic stability and stabilization of dynamic interval systems"

10.1109/TAC.2004.841921IEEE Transactions on Automatic Control502276-277IETA