Invariance Kernels of Single-Input Planar Nonlinear Systems

Computing Invariance Kernels of Polygonal Hybrid Systems

Polygonal hybrid systems are a subclass of planar hybrid automata which can be represented by piecewise constant differential inclusions. One way of analysing such systems (and hybrid systems in general) is through the study of their phase portrait, which characterise the systems’ qualitative behaviour. In this paper we identify and compute an important object of polygonal hybrid systems’ phase...

Robust Adaptive Control of Linearizable Nonlinear Single Input Systems

The design of stabilizing controllers for nonlinear plants with unknown nonlinearities is a challenging problem. The inability to identify exactly the nonlinearities on-line or off-line motivates the design of stabilizing controllers based on approximations or on approximate estimates of the plant nonlinearities. The price paid in such case, could be lack of theoretical guarantees for global st...

Continuous Stabilizing of First Order Single Input Nonlinear Systems

In this paper, stabilizability of first order nonlinear systems by a smooth control law is investigated. The main results are presented by the examples and finally summarized in a lemma. The proof for the lemma is according to Sontag’s formula. In addition, it is explained that using weak control Lyapunov functions in Sontag’s formula generates (possibly nonsmooth) the control law, which global...

Invariance Control of Noncascade Nonlinear Systems

This paper addresses the problem of controlling a state space region positively invariant while guaranteeing asymptotic stability for a class of nonlinear noncascade systems. Therefore a nonsmooth feedback controller is developed, achieving dissipa-tivity of the linear subsystem. This in turn allows switching of a control parameter of an additional asymptotic stabilizing control law. The freedo...

Structure Invariance for Uncertain Nonlinear Systems