Controllers For Discrete-time Linear Parameter-varying Systems Research Articles

On the Necessity of LMI-Based Design Conditions for Discrete Time LPV Filters

In this note, we provide a proof of necessity for one of the results in [W. M. H. Heemels, J. Daafouz, and G. Millerioux, “Observer-based control of discrete-time LPV systems with uncertain parameters,” Automatic Control, IEEE Transactions on, vol. 55, no. 9, pp. 2130–2135, 2010]. This result is essential to the design of discrete-time linear parameter varying (LPV) filters using parameter-dependent poly-quadratic Lyapunov functions. We also provide a brief discussion ofits broader implications on the design of discrete-time LPV filters.

Fixed-structure LPV discrete-time controller design with induced l2-norm and performance

ABSTRACTA new method for the design of fixed-structure dynamic output-feedback linear parameter-varying (LPV) controllers for discrete-time LPV systems with bounded scheduling parameter variations is presented. Sufficient conditions for the stability, and induced l2-norm performance of a given LPV system are represented through a set of linear matrix inequalities (LMIs). These LMIs are used in an iterative algorithm with monotonic convergence for LPV controller design. Extension to the case of uncertain scheduling parameter value is considered as well. Controller parameters appear directly as decision variables in the optimisation program, which enables preserving a desired controller structure in addition to the low order. Efficiency of the proposed method is illustrated on a simulation example, with an iterative convex optimisation scheme used for the improvement of the control system performance.

Gain-Scheduled State Feedback Controllers for Discrete-Time LPV systems Using Scheduling Parameters Affected by Absolute and Proportional Uncertainties

This paper is concerned with the design problem of Gain-Scheduled State Feedback (GSSF) controllers for discrete-time Linear Parameter-Varying (LPV) systems. By considering that exact scheduling parameters are not available in many practical systems, the scheduling parameters provided to GSSF controllers are supposed to be affected by absolute as well as proportional uncertainties. We introduce a set covering the admissible set for the pair of scheduling parameters and the inexact ones, and propose a design method of GSSF controllers using the set. Numerical examples illustrate the effectiveness and possible conservatism of our method.

Robust Fixed-order Discrete-time LPV Controller Design

A new method for the design of fixed-order dynamic output-feedback Linear Parameter Varying (LPV) controllers for discrete-time LPV systems with bounded scheduling parameter variations is presented. Sufficient conditions for stability and induced l2-norm performance of an LPV system are given through a set of Linear Matrix Inequalities (LMIs) and exploited for design. Controller parameters appear directly as decision variables in the convex optimisation program, which enables preserving a desired controller structure in addition to the low order. Efficiency of the proposed method is illustrated on a simulation example, with an iterative convex optimisation scheme used for the control system performance improvement.

Induced L2 Norm Improvement by Interpolating Controllers for Discrete-time LPV Systems

The paper shows an interpolation-based control solution asapossible technique to formulate the constrained H∞ control problem for discrete-time linear parameter varying (LPV) systems. The control policy is constructed by interpolating amongapriori designed, unconstrained, constant, state feedback controllers. Invariant set theory is used to introduce the measure of the domain of applicability. It is shown that the `trade-off' between the performance and the size of the domain of applicability can be significantly reduced by controller interpolation. Hence, the interpolation-based controller becomes applicable overamuch larger region than any other single state feedback. The proposed method gives stabilizing solution not only under hard constraints, but also allows the online modification of the induced L² norm from the generalized disturbance input to the predefined performance output. Moreover, the suggested method can be applied in real-time environment.