A direct and converse Lyapunov theorem for a nonlinear 2D discrete system described by the Fornasini-Marchesini second model2020 · A direct and converse Lyapunov theorem for an autonomous nonlinear 2D discrete system described by the Fornasini-Marchesini second model has been obtained in this note. The Fornasini-Marchesini second model is re-formulated as a non-linear operator in an infinitedimensional space, and the Lyapunov theorem is stated and proved in this setup. The result then extended to ND systems with any N >= 2.
Existence of an observation window of finite width for continuous-time autonomous nonlinear systems2016 · In this note, the relationship between notions of observability for continuous-time nonlinear system related to distinguishability, observability rank condition and K-function has been investigated. It is proved that an autonomous nonlinear system that is observable in both distinguishability and rank condition sense permits an observation window of finite width, and it is possible to construct a K-function related to observability for such system. (C) 2016 Elsevier Ltd. All rights reserved.
Controllability to the origin implies state-feedback stabilizability for discrete-time nonlinear systems2016 · The problem of finite-time state-feedback stabilizability of discrete-time nonlinear systems has been considered in this technical communique. Two assertions have been proved. First, if the system is N-step controllable to the origin, then there is a state feedback control law for which the trajectory of the closed-loop system converges to the origin in N steps. Second, if the system is asymptotically controllable to the origin and satisfies the controllability rank condition at the origin, then there is a state feedback control law for which the trajectory of the closed-loop system converges to the origin in finite steps. (C) 2016 Elsevier Ltd. All rights reserved.
