Publication

Fixed-order H-infinity and H-2 Controller Design for Continuous-time Polytopic Systems: An LMI-based Approach

Alireza Karimi
2013
Conference Papers

Abstract

In this paper, a convex set of fixed-order H-infinity and H2 dynamic output-feedback controllers for continuous-time systems with polytopic uncertainty is proposed. This approach is based on the use of some instrumental stable matrices, which operate as a tool to decouple the controller parameters and the Lyapunov matrices. Then, the stability of the closed-loop system as well as H-infinity and H2 performance criteria are expressed by a set of linear matrix inequalities based upon linearly parameter-dependent Lyapunov matrices. Iterative procedure for updating the instrumental matrices using the previous controller can increase the performance of the approach. Simulation results demonstrate the effectiveness of the proposed method.

Official source

https://infoscience.epfl.ch/entities/publication/d860fb05-ed17-4f97-99e9-d04f0bbe0bfe

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Alireza Karimi
2013
Conference Papers

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/d860fb05-ed17-4f97-99e9-d04f0bbe0bfe

About this result

Related concepts (32)

Matrix (mathematics)

In mathematics, a matrix (plural matrices) is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object. For example, is a matrix with two rows and three columns. This is often referred to as a "two by three matrix", a " matrix", or a matrix of dimension . Without further specifications, matrices represent linear maps, and allow explicit computations in linear algebra.

Closed-loop controller

A closed-loop controller or feedback controller is a control loop which incorporates feedback, in contrast to an open-loop controller or non-feedback controller. A closed-loop controller uses feedback to control states or outputs of a dynamical system. Its name comes from the information path in the system: process inputs (e.g., voltage applied to an electric motor) have an effect on the process outputs (e.g., speed or torque of the motor), which is measured with sensors and processed by the controller; the result (the control signal) is "fed back" as input to the process, closing the loop.

Lyapunov stability

Various types of stability may be discussed for the solutions of differential equations or difference equations describing dynamical systems. The most important type is that concerning the stability of solutions near to a point of equilibrium. This may be discussed by the theory of Aleksandr Lyapunov. In simple terms, if the solutions that start out near an equilibrium point stay near forever, then is Lyapunov stable. More strongly, if is Lyapunov stable and all solutions that start out near converge to , then is said to be asymptotically stable (see asymptotic analysis).

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