L/sub 2/-gain analysis of nonlinear systems and nonlinear state-feedback H/sub infinity / control

1992/06/01 by Arjan van der Schaft, A.J. van der Schaft · 1,576 citations
Engineering · Mathematics · #Adaptive Control of Nonlinear Systems #Applied mathematics #Computer science #Control (management) #Control and Stability of Dynamical Systems #Control theory (sociology) #Hamiltonian (control theory) #Infinity #Invariant (physics) #Mathematical analysis #Mathematical optimization #Mathematical physics #Mathematics #Nonlinear control #Nonlinear system #Physics #Pure mathematics #Stability and Control of Uncertain Systems #State space

paper · open access · doi:10.1109/9.256331

published in IEEE Transactions on Automatic Control 37(6), 770-784 (Institute of Electrical and Electronics Engineers)

openalex publication_date 1992/06/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30

Abstract

Previously obtained results on L2-gain analysis of smooth nonlinear systems are unified and extended using an approach based on Hamilton-Jacobi equations and inequalities, and their relation to invariant manifolds of an associated Hamiltonian vector field. On the basis of these results a nonlinear analog is obtained of the simplest part of a state-space approach to linear H/sub infinity / control, namely the state feedback H/sub infinity / optimal control problem. Furthermore, the relation with H/sub infinity / control of the linearized system is dealt with.>

Citations

• Dissipative dynamical systems Part II: Linear systems with quadratic supply rates
• Dissipative dynamical systems part I: General theory

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