Analysis of LPV systems using a piecewise affine parameter-dependent Lyapunov function

2002 ◽  
Author(s):  
Sungyung Lim ◽  
J.P. How
Keyword(s):  
Lyapunov Function ◽  
Piecewise Affine ◽  
Lpv Systems ◽  
Affine Parameter ◽  
Parameter Dependent

Robust H 2 Performance of LPV Systems Via Parameter Dependent Lyapunov Function

2000 ◽  
Vol 33 (14) ◽  
pp. 415-420
Author(s):  
J. de Oliveira ◽  
A. Trofino ◽  
C.E. de Souza
Keyword(s):  
Lyapunov Function ◽  
Lpv Systems ◽  
Parameter Dependent

Control of a small helicopter with linear matrix inequality-based design assuring stability and performance

2019 ◽  
Vol 234 (3) ◽  
pp. 624-639
Author(s):  
İsmail Hakkı Şahin ◽  
Coşku Kasnakoğlu
Keyword(s):  
Lyapunov Function ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Linear Parameter ◽  
Common Lyapunov Function ◽  
Affine Parameter ◽  
Dependent Model ◽  
And Performance ◽  
Parameter Dependent ◽  
Grid Based

This article focuses on linear matrix inequality-based controller designs that can achieve stabilization and reference tracking for a small unmanned helicopter at various flight conditions. A nonlinear mathematical model of a small-scale helicopter is constructed. Then trim conditions are found and linearized around different equilibrium points. Local [Formula: see text] controllers are designed at trim conditions based on the local linear models. The pointwise controllers achieve local stability and performance, but fail at stabilization and tracking over the full envelope. A scheduling controller is built by blending the local controller outputs. In addition, grid-based [Formula: see text] controllers are designed at each operating point with common Lyapunov function. This allows controller scheduling between the adjacent design points with guaranteed stability and performance across the design envelope. Based on the family of linear systems which are obtained from the nonlinear model, an affine parameter-dependent model is built to exploit the approximate linear parameter dependency. Then, a parameter-dependent linear parameter varying controller is synthesized for the affine parameter-dependent model. Although local performance is satisfactory for all given design methods, local [Formula: see text] controllers and affine parameter-dependent controller cannot yield satisfactory performance over the full flight envelope apart from the grid-based controller with common Lyapunov function approach.

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