Simple robust stabilisation of nonlinear systems

The robust stabilization problem is solved by constructing variable structure state-feedback control laws based on a conic partition of the state-space. The control Lyapunov function candidate and the conic partition are induced by a polyhedral region of interest. Nonlinear systems are approximated as piecewise affine in every sub-region of the partition. The partition has a simple and systematic form, and independent local design in a computationally tractable manner is possible. Piecewise-linear Lyapunov function candidates are used, which offer ease in addressing robustness to bounded uncertainties. Simple linear programming problems are utilized for computing controls offering optimal performance under control constraints and approximation errors.