Stabilization of LPV Systems: State Feedback, State Estimation, and Duality

Abstract

In this paper, the problem of the stabilization of Linear Parameter Varying systems by means of Gain Scheduling Control, is considered This technique consists on designing a controller which is able to update its parameters on-line according to the variations of the plant parameters. We first consider the state feedback case and we show a design procedure based on the construction of a Lyapunov function for discrete-time LPV systems in which the parameter variations are affine and occur in the state matrix only. This procedure produces a nonlinear static controller. We show that, differently from the robust stabilization case, we can always derive a linear controller, that is nonlinear controllers cannot outperform linear ones for the gain scheduling problem. Then we show that this procedure has a dual version which leads to the construction of a linear gain scheduling observer. The two procedures may be combined to derive an observer-based gain scheduling compensator.

A New LMI-Based Output Feedback Controller Design Method for Discrete-Time LPV Systems with Uncertain Parameters

“…For the case of continuous-time LPV systems, see for instance, Apkarian and Adams (1998), Kose and Jabbari (1999), Balas et al (2004), Scorletti and El Ghaoui (1995), Wu (2001), Gilbert et al (2010), Sato (2011), Song and Yang (2011). Also, for the discretetime dynamic output feedback controller LPV systems, see for instance, Blanchini and Miani (2003), De Caigny et al (2012), Zhang et al (2009), Emedi andKarimi (2014), De Oliveira et al (1999), Oliveira and Peres (2005)). Hence, the investigation of LPV systems with inexact but bounded parameters attracts the attention of many researchers in this field Wu et al (1997), Kalsi et al (2010).…”

Design of observer-based controllers for LPV systems with unknown parameters

“…Linear Parameter-Varying (LPV) systems have received considerable attention from the control community in recent years due to their applicability in many practical situations (see [1], [2], [3], [4], [5], [6] and references therein). Controllers that are designed on the basis of LPV system models have to satisfy two important properties, when they are implemented in practice:…”

Análise e síntese de sistemas LPV polinomiais homogêneos usando funções de Lyapunov dependentes de sucessivos instantes de tempo

“…conjunto de todas as N -uplas de números naturais cuja soma é igual a g , 1991;SCHERER, 2001;MIANI, 2003;DE-CAIGNY et al, 2007;MONTAGNER et al, 2009;BORGES et al, 2010a). Isto decorre do fato de que os sistemas LPV podem ser usados para representar uma vasta gama de problemas do mundo real, cuja dinâmica é regida por parâmetros que variam com o tempo (PAIJMANS et al, 2008;DE-CAIGNY et al, 2009;DE-CAIGNY et al, 2010b).…”