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

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11.2  Discrete-Time Mixed H2/H Nonlinear Control

In this section, we discuss the state-feedback mixed H2/H-control problem for discrete-time nonlinear systems. We begin with an affine discrete-time state-space model defined on Xn in coordinates (x1,…,xn) :

da:{ x˙k+1=f(xk)+g1(xk)wk+g2(xk)uk;x(k0)=x0zk=h1(xk)+k12(xk)ukyk=xk,

(11.29)

where all the variables and system matrices have their previous meanings and dimensions respectively. We assume similarly that the system has a unique equilibrium at x = 0, and is such that f(0) = 0 and h10) = 0. For simplicity, we similarly also assume the following hold for the system matrices.

Assumption 11.2.1 The system matrices are such that

h1T

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