Gain-Scheduledℋ2Controller Synthesis for Continuous-Time Polytopic LPV Systems

Guangbin Cai,Huafeng He,Changhua Hu,Xiaojun Han,Baojuan Yin

doi:10.1155/2014/972624

Abstract

This paper is concerned with the problem of gain-scheduledℋ2controller synthesis for continuous-time linear parameter-varying systems. In this problem, the system matrices in the state-space form are polytopic and patameterized and the admissible values of the parameters are assumed to be measurable on-line in a polytope space. By employing a basis-parameter-dependent Lyapunov function and introducing some slack variables to the well-established performance conditions, sufficient conditions for the existence of the desired gain-scheduledℋ2state feedback and dynamic output feedback controllers are established in terms of parameterized linear matrix inequalities. Based on the polytopic characteristic of the dependent parameters and a convexification method, the corresponding controller synthesis problem is then cast into finite-dimensional convex optimization problem which can be efficiently solved by using standard numerical softwares. Numerical examples are given to illustrate the effectiveness and advantage of the proposed methods.

Highlights

It is well known that linear parameter-varying (LPV) systems are a class of linear systems whose state-space matrices depend on a set of time-varying parameters which are not known in advance but can be measured or estimated upon operation of the systems
There are many examples of parameter-dependent systems in practice, such as in aeronautics, aerospace, mechanics, and industrial processes. This has motivated extensive studying of the gain-scheduled analysis and controller synthesis methods for various LPV systems from many aspects, including continuous-time and discrete-time systems, statespace formula and linear fractional transformation representation, affine-type and polytopic systems, state feedback and output feedback controllers, quadratic Lyapunov functionbased and parameter-dependent Lyapunov function-based methods, and robust H2 and H∞ control performances
For the sake of reducing the abovementioned conservativeness, several control methods have been developed in the past decade, such as gain-scheduled H2 and H∞ control based on parameter-dependent Lyapunov function (PDLF) method

Summary

Introduction

It is well known that linear parameter-varying (LPV) systems are a class of linear systems whose state-space matrices depend on a set of time-varying parameters which are not known in advance but can be measured or estimated upon operation of the systems. In most of the existing work, the gain-scheduled LPV control synthesis problems are performed through semidefinite programming and especially linear matrix inequality (LMI) techniques [2, 5,6,7,8, 10, 15,16,17, 19, 26] This is due mainly to the fact that a number of methods of gain-scheduled control design for LPV systems proposed in the literature are based on small-gain approach (see, e.g., [1,2,3,4, 17]) or on the notions of quadratic Lyapunov function (see, e.g., [1, 7, 28]). If their dimensions are not explicitly stated, are assumed to be compatible for algebraic operations

Problem Description and Preliminaries

Gain-Scheduled H2 Control Design

State Feedback Control Design

Dynamic Output Feedback Control Design

Illustrative Example

Conclusions