In this paper, we study controlled homogeneous dynamical systems and derive conditions under which the system is perspective controllable. We also derive conditions under which the system is observable in the presence of a control over the complex base field. In the absence of any control input, we derive a necessary and sufficient condition for observability of a homogeneous dynamical system o...

Complexity is a systemic property. Adaptive evolving systems like ethnic cliques or complex social situations such as “knife crimes” are best understood as dynamic networks of interactions and relationships, not mere aggregates of static entities that can by analyzed by separately identifying and enumerating them. By definition, relata do not exist in individual particles, only in their inter-r...

This paper studies output feedback control of pure-feedback systems with immeasurable states and completely non-affine property. Since availability of all the states is usually impossible in the actual process, we assume that just the system output is measurable and the system states are not available. First, to estimate the immeasurable states a state observer is designed. Relatively fewer res...

Preface This text is a slightly edited version of lecture notes for a course I gave at ETH, during the Winter term 2000-2001, to undergraduate Mathematics and Physics students. The choice of topics covered here is somewhat arbitrary, and was partly imposed by time limitations. Evidently, these notes do not intend to replace the many existing excellent textbooks on the subject, a few of which ar...

this paper concerns the problem of robust stabilization of uncertain fractional-order non-autonomous systems. in this regard, a single input active control approach is proposed for control and stabilization of three-dimensional uncertain fractional-order systems. the robust controller is designed on the basis of fractional lyapunov stability theory. furthermore, the effects of model uncertainti...

It is generally believed that the dynamics of simple fluids can be considered to be chaotic, at least to the extent that they can be mod-eled as classical systems of particles interacting with short range, repulsive forces. Here we give a brief introduction to those parts of chaos theory that are relevant for understanding some features of non-equilibrium processes in fluids. We introduce the n...

We present two codimension-one bifurcations that occur when an equilibrium collides with a discontinuity in a piecewise smooth dynamical system. These simple cases appear to have escaped recent classifications. We present them here to highlight some of the powerful results from Filippov’s book Differential Equations with Discontinuous Righthand Sides (Kluwer, 1988). Filippov classified the so-c...