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

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6.4    Output Measurement-Feedback H-Control for a General Class of Nonlinear Systems

In this section, we look at the output measurement-feedback problem for a more general class of nonlinear systems. For this purpose, we consider the following class of nonlinear systems defined on a manifold Xn containing the origin in coordinates x = (x1, …, xn):

Σg:{ x˙=F(x,w,u);x(t0)=x0z=Z(x,u)y=Y(x,w)

(6.52)

where all the variables have their previous meanings, while F:X×W×UX is the state dynamics function, Z:X×Us is the controlled output function and Y:X×Wm is the measurement output function. Moreover, the functions F (., ., .), Z(., .) and Y (., .) are smooth Cr, r ≥ 1 functions of their arguments, and the point x = 0 ...

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