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Nonlinear H-Infinity Control, Hamiltonian Systems and Hamilton-Jacobi Equations by M.D.S. Aliyu

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5.3    Robust Nonlinear H State-Feedback Control

In this section, we consider the state-feedback H-control problem for the affine nonlinear system Σa in the presence of unmodelled dynamics and/or parameter variations. This problem has been considered in many references [6, 7, 209, 223, 245, 261, 265, 284]. The approach presented here is based on [6, 7] and is known as guaranteed-cost control. It is an extension of quadratic-stabilization, and was first developed by Chang [78] and later popularized by Petersen [226, 227, 235]. For this purpose, the system is represented by the model:

ΣΔa:{ x˙=f(x)+Δf(x,θ,t)+g1(x)w+[ g2(x)+Δg2(x,θ,t) ]u;x(t0)=x0y=xz=[ h1(x)u]

(5.41)

where all the variables ...

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