In this Letter, a dynamical delayed output-feedback (DDOF) control strategy is proposed for stabilizing unstable periodic orbits (UPOs) of chaotic systems. Using the Floquet theory, a separation principle is established which gives a necessary and sufficient stability condition for DDOF UPO stabilizing control systems. The new principle shows that the so-called "odd number limitation" for delayed state-feedback control systems also applies to DDOF control.

A general dynamic model is proposed for describing a large class of nonholonomic systems including extended chained systems, extended power systems, underactuated surface vessel systems etc. By introducing an assistant state variable and a time-varying state transformation based on the concept of minimal dilation degree, this class of nonholonomic systems is transformed into linear time-varying control systems, and the asymptotic exponential stability is thus achieved by using a smooth time-varying feedback control law. The existence and uniqueness of the minimal dilation degree for the discussed systems are also proved under certain conditions.

This paper addresses the robust learning control problem for a class of nonlinear systems with structured periodic and unstructured aperiodic uncertainties. A recursive technique is proposed which extends the backstepping idea to the robust repetitive learning control systems. A learning evaluation function instead of a Lyapunov function is formulated as a guideline for derivation of the control strategy which guarantees the asymptotic stability of the tracking system. A design example is given.

Based on the clockwise property of parameterized curves and the general Nyquist criterion of stability, a conjecture on the stability of the Internet congestion control algorithm with diverse propagation delays is proved. A more general stability criterion is also provided. The new criterion preserves the elegancy of the conjecture being decentralized and locally implemented: each end system needs knowledge only of its own round-trip delay, but enlarges the stability region of control gains and admissible communication delays.

In this brief, an adaptive chaos control method is developed for stabilizing chaotic systems at their unknown equilibrium(s) using the invariant manifold theory. The developed method overcomes the problem that the equilibrium(s) of the chaotic systems are dependent on the unknown system parameters, which makes direct application of the conventional adaptive control difficult. Further development of the adaptive chaos control is undertaken for the situation where the parameter estimates are only allowed to vary within a bounded set due to the sensitivity of chaotic systems to parameter variations. A sufficient condition for convergence of system states and parameter estimates is obtained. The design method developed then is applied to stabilizing the Lorenz chaotic system at an unknown equilibrium. Both mathematical and computational results have demonstrated the effectiveness of this method.