For polynomial systems, programming uses semidefinite optimization to search for Lyapunov functions of a fixed degree (e.g., quartic). Toolboxes like SOSTOOLS (MATLAB) or SumOfSquares.jl (Julia) automate robust nonlinear design. Example: find (V(\mathbfx)) and control (u(\mathbfx)) such that:
For control systems (\dot\mathbfx = \mathbff(\mathbfx) + \mathbfg(\mathbfx)\mathbfu), a is a (V(\mathbfx) > 0) such that for every (\mathbfx \neq 0): : Serves as a reference for contemporary work
Synchronizing power converters in smart grids despite fluctuating solar and wind inputs. Instead of analyzing a given system, the engineer
: Serves as a reference for contemporary work and a source for new research problems in robust nonlinear control. Design Engineers Instead of analyzing a given system
One of the book's primary contributions is identifying and mitigating the "curse" of excessive control effort in traditional Lyapunov designs. Amazon.com Constructive Lyapunov Redesign
In the context of , this theory is inverted. Instead of analyzing a given system, the engineer constructs the control law $u$ specifically to make $\dotV$ negative. This is known as Lyapunov-based control design (often implemented via Control Lyapunov Functions, or CLFs).