Nonlinear H-Infinity Control, Hamiltonian Systems and Hamilton-Jacobi Equations

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State-Feedback Nonlinear ${\mathcal{H}}_{\infty }$-Control for Continuous-Time Systems

In this chapter, we discuss the nonlinear ${\mathcal{H}}_{\infty }$ sub-optimal control problem for continuous-time affine nonlinear systems using state-feedback. This problem arises when the states of the system are available, or can be measured directly and used for feedback. We derive sufficient conditions for the solvability of the problem, and we discuss the results for both time-invariant (or autonomous) systems and time-varying (or nonautonomous) systems, as well as systems with a delay in the state. We also give a parametrization of all full-information stabilizing controllers for each system. Moreover, understanding the state-feedback problem will facilitate the understanding of the dynamic ...