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This paper provides an introduction to several problems and techniques related to controlling periodic motions of dynamical systems. In particular, we define and discuss problems of motion planning and orbit planning, analysis methods such as the classical Poincaré first-return map and the transverse linearization, and exponentially orbitally stabilizing… (More)
In this paper we study the well-posedness (existence and uniqueness of solutions) of linear relay systems with respect to two diierent solution concepts, Filippov solutions and forward solutions. We derive necessary and suucient conditions for well-posedness in the sense of Filippov of linear systems of relative degree one and two in closed loop with relay… (More)
We review and pay tribute to a result on convergent systems by the Russian mathematician Boris Pavlovich Demidovich. In a sense, Demidovich's approach forms a prelude to a ÿeld which is now called incremental stability of dynamical systems. Developments on incremental stability are reviewed from a historical perspective.
The paper deals with the problem of estimation of the topological entropy for non-autonomous systems of differential equations via the second (direct) Lyapunov method. The main result of the paper is illustrated by examples concerning the Lorenz system and Duffing oscillator.