D-stable controller design for Lipschitz NLPV system

Conference Article


IFAC Workshop on Linear Parameter-Varying Systems (LPVS)





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This paper addresses the design of a state-feedback controller for a class of nonlinear parameter varying (NLPV) systems in which the nonlinearity can be expressed as a parameter-varying Lipschitz term. The controller is designed to satisfy a D-stability specification, which is akin to imposing constraints on the closed-loop pole location in the case of LTI and LPV systems. The design conditions, obtained using a quadratic Lyapunov function, are eventually expressed in terms of linear matrix inequalities (LMIs), which can be solved efficiently using available solvers. The effectiveness of the proposed method is demonstrated by means of a numerical example.


control nonlinearities, control system synthesis, control theory.

Author keywords

Pole placement, D-stability, gain-scheduling, linear matrix inequalities (LMIs), Lipschitz nonlinear systems, nonlinear parameter varying (NLPV) systems, controller design

Scientific reference

R. Yang, D. Rotondo and V. Puig. D-stable controller design for Lipschitz NLPV system, 3rd IFAC Workshop on Linear Parameter-Varying Systems, 2019, Eindhoven, The Netherlands, Vol 52:28 of IFAC Papers Online, pp. 88-93.