Polynomial LPV approach to robust H_∞ control of nonlinear sampled-data systems

Abstract

This paper addresses $L_2$-gain analysis and robust $H_{\mathrm{\infty }}$ control of nonlinear sampled-data systems described by a polynomial linear parameter varying (PLPV) model. First, conditions for $L_2$-gain analysis of sampled-data PLPV systems are derived using a modified Krasovskii functional in which the distance between the real and measured parameters are considered as uncertainties. The resulting conditions are formulated in terms of parameterised linear matrix inequalities (PLMI). Second, a solution approach for satisfying PLMI conditions over the set of whole parameters and uncertainties is proposed using the sum-of-squares decomposition method. Third, conditions for robust $H_{\mathrm{\infty }}$ sampled-data controller synthesis for nonlinear systems described by PLPV models are derived in terms of parameterised bilinear matrix inequalities (PBMI) with the maximum allowable sampling period as the parameter. To make the resulting bilinear matrix inequality (BMI) problems tractable, an iterative algorithm is developed and utilised to solve the problem. Finally, the effectiveness of the proposed approach is verified using several real-world examples.

Keywords:

• Sampled-data systems
• robust $H_{\mathrm{\infty }}$ controller
• SOS decomposition
• PLMI
• Krasovskii functional

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Kaveh Hooshmandi  http://orcid.org/0000-0003-1735-9856

Farhad Bayat  http://orcid.org/0000-0001-5131-3419

Notes

1 The quasi- prefix is used to indicate LPV system models in which the parameters are chosen to be endogenous, i.e. dependent of the inputs, outputs or additional latent variables of the modelled physical system (Hoffmann & Werner, 2015).