Nonsmooth Stabilizability and Feedback Linearization of Discrete - Time Nonlinear Systems
نویسنده
چکیده
We consider the problem of stabilizing a discrete-time nonlinear system using a feedback which is not necessarily smooth. A sufficient condition for global dynamical stabilizability of single-input triangular systems is given. We obtain conditions expressed in terms of distributions for the nonsmooth feedback triangularization and linearization of discrete-time systems. Relations between stabilization and linearization of discrete-time systems are given.
منابع مشابه
Asymptotic Controllability and Exponential Stabilization of Nonlinear Control Systems at Singular Points
We discuss the relation between exponential stabilization and asymptotic controllability of nonlinear control systems with constrained control range at singular points. Using a discounted optimal control approach, we construct discrete feedback laws minimizing the Lyapunov exponent of the linearization. Thus we obtain an equivalence result between uniform exponential controllability and uniform...
متن کاملQuadratic Stabilization of Nonlinear Discrete Time Control Systems with Uncontrollable Linearization
In this paper we study the problem of stabilization of nonlinear systems with uncontrollable linearization. The use of normal forms, permit to nd conditions on controllability and stabilizability. We remark that conditions on controllability and stabilizability are intimately related to a set of quadratic invariants.
متن کاملStabilization of Discrete Time Systems with a Fold or Period Doubling Control Bifurcations
For nonlinear control systems with uncontrollable linearization around an equilibrium, the local asymptotic stability of the linear controllable directions can be easily achieved by linear feedback. Therefore we expect that the stabilizability of the whole system should depend on a reduced order model whose stabilizability depends on the linearly uncontrollable directions. The controlled center...
متن کاملTime-Invariant State Feedback Control Laws for a Special Form of Underactuated Nonlinear Systems Using Linear State Bisection
Linear state bisection is introduced as a new method to find time-invariant state feedback control laws for a special form of underactuated nonlinear systems. The specialty of the systems considered is that every unactuated state should be coupled with at least two directly actuated states. The basic idea is based on bisecting actuated states and using linear combinations with adjustable parame...
متن کاملFeedback linearization and lattice theory
The tools of lattice theory are applied to readdress the static state feedback linearization problem for discrete-time nonlinear control systems. Unlike the earlier results that are based on differential geometry, the new tools are also applicable for nonsmooth systems. In case of analytic systems, close connections are established between the new results and those based on differential one-for...
متن کامل