Improved ℋ<sub>2</sub>and ℒ<sub>2</sub>control designs for discrete-time LPV/LFR systems
Renan Lima Pereira, Matheus Senna de Oliveira
Abstract
This paper addresses novel H2 and L2 norm-based controller designs for discrete-time linear parameter-varying (LPV) systems with linear fractional representation (LFR). Despite the importance of LPV/LFR systems to the control literature, there is a lack of works on this topic. The distinctive formulation of the proposed controller designs is given by using parameter-dependent Lyapunov functions in combination with slack variables and general full-block multipliers. Such proposed formulation leads to less conservative synthesis conditions characterised in terms of a finite number of linear matrix inequalities for both state-feedback and static output-feedback controllers subject to H2 and L2 performances for discrete-time LPV/LFR systems. Improvements obtained by the proposed controller design conditions over existing methods in the area are assessed by numerical examples.