Gain-scheduled ℋ2 controller synthesis for linear parameter varying systems via parameter-dependent Lyapunov functions

Abstract

SUMMARYThis paper deals with the problem of gain-scheduled H 2 control for linear parameter-varying systems. The system state-space model matrices are affinely parameterized and the admissible values of the parameters and their rate of variation are supposed to belong to a given convex bounded polyhedral domain. Based on a parameter-dependent Lyapunov function, a linear matrix inequality methodology is proposed for designing a gain-scheduled state feedback H 2 controller, where the feedback gain is a matrix fraction of polynomial matrices with quadratic dependence on the scheduling parameters.

A vibroacoustic application of modeling and control of linear parameter-varying systems

“…This choice has the advantage that the LPV model H(θ) given by model (1) can be used in LPV control synthesis techniques for affine LPV models (for example, Amato et al, 2005;Apkarian et al, 1995;de Souza and Trofino, 2006;Lu et al, 2008) as well as in the linear fractional transformation framework (for example, Packard, 1994;Scherer, 2001). Moreover, when θ is bounded, model (1) can be converted exactly in a polytopic LPV model 1 with two vertices, which is useful since control synthesis for polytopic models has been widely studied (De Caigny et al, 2008a, 2008bLeite and Peres, 2004;Montagner et al, 2007;Oliveira and Peres, 2008).…”

Synchronization of nonlinear master–slave systems under input delay and slope‐restricted input nonlinearity

“…Linear parameter varying (LPV) method is a new and less conservative approach for design, analysis, and synthesis of feedback controllers for nonlinear systems. In the past few years, LPV approach has received more attention as it has been successfully applied to the gain scheduling, H 1 controller design [23,24], system identification, and state feedback control [25,26].…”

“…To design a controller applicable to both small and large input delays, the delay-rangedependent control approach, rather than the conventional delay-dependent and delay-independent methodologies, is adopted by considering time-varying nature of the input delay. Based on an intricate Lyapunov-Krasovskii (LK) functional [15], rigorous matrix algebra, LPV approach [24][25][26], properties of nonlinear dynamics, and Jensen's inequality [27], a state-feedback control design schema is derived. The feedback controller gain for the synchronization controller can be determined by solving matrix inequalities for feasibility problem to achieve asymptotic synchronization of the master-slave systems.…”

A BMI approach for ℋ︁∞ gain scheduling of discrete time‐varying systems

“…As a way to guarantee robustness against practical disturbances, the H 2 and H ∞ norms have been frequently applied as indexes of performance. Recent works include [13] where the problem of stabilizability and H ∞ control of discrete-time LPV systems is investigated by means of gain-scheduled state feedback [14] in which gain scheduling for linear fractional transformation (LFT) systems is designed by using parameter-dependent Lyapunov functions [15], where gain scheduled H 2 controllers for affine LPV systems are proposed [16] in which robust and gainscheduled controllers for LFT parameter-dependent systems are designed by using duality theory [17], where switching H ∞ controllers for a class of LPV systems scheduled along a measurable parameter trajectory are addressed, among others.…”