For a nonlinear system, the stability around an equilibrium point can be established if one can find a Lyapunov function. Nonlinear control design can be carried out by exploring the possibility of making a Lyapunov function candidate as a Lyapunov function through control design. In this chapter, we start with the fundamental form of adding an integrator, and then introduce the method for iterative backstepping with state feedback. We also introduce backstepping using output feedback, and adaptive backstepping for certain nonlinear systems with unknown parameters.

Chapter Contents:

• 9.1 Integrator backstepping
• 9.2 Iterative backstepping
• 9.3 Observer backstepping
• 9.4 Backstepping with filtered transformation
• 9.5 Adaptive backstepping
• 9.6 Adaptive observer backstepping

Inspec keywords: Lyapunov methods; state feedback; control system synthesis; nonlinear control systems; adaptive control; stability

Other keywords: Lyapunov function; state feedback; adaptive backstepping; stability; equilibrium point; integrator; nonlinear control system; iterative backstepping design; output feedback; unknown parameters

Subjects: Control system analysis and synthesis methods; Stability in control theory; Nonlinear control systems