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

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3.5    Dissipativity and Passive Properties of Discrete-Time Nonlinear Systems

In this section, we discuss the discrete-time counterparts of the previous sections. For this purpose, we again consider a discrete-time nonlinear state-space system defined on X ⊆ ℜn containing the origin x = {0} in coordinates (x = x1,…, xn):

d:{ xk+1=f(xk,uk),x(k0)=x0yk=h(xk,uk)

(3.59)

where xkX is the state vector, ukU ⊆ ℜm is the input function belonging to an input space U, ykYm is the output function which belongs to the output space Y (i.e., Σd is square). The functions f : X × UX and h : X × UY are real Cr functions of their arguments such that there exists a unique solution x(k, k0, x0, uk) to the system ...

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