This paper proposes a new framework of stability analysis for linear time-invariant discrete-time systems based on experimental input and output data, in which no mathematical model such as a state equation or transfer function is employed unlike conventional model-based stability analyses. In this framework, we first develop a data-based stability condition for open-loop systems by using a set of output data of a zero-input response, which constitutes a basis of the entire output data space. Then, we consider an output feedback control law and present a data-based stability condition for closed-loop systems by using a set of input and output data of the controlled system, whose linear combinations span the entire closed-loop data space. Both of these data-based stability conditions are derived by the Lyapunov's second method and enable us to investigate stability of dynamical systems directly from the behaviors, i.e., the input and output data.
This paper proposes a brand new active control panel system for reducing the floor impact noise, which is a main object of interest by residents in condominium in Japan. The active control of floor impact noise is realized by covering whole area of ceiling with the active panels of modular type, each of which insulates independently the impact sound emitted from the concrete slab structure. The active panel of 0.9 [m] ×0.9 [m] in dimension is comprised of light-weighted panel of honey-comb structure, five piezoelectric actuators and five acceleration sensors. A new actuator mechanism is developed, which has heterogeneous structure of piezo-electric element of bimorph type and soft plates of same size for mechanical reinforcement, and provides with the maximized displacement. The active control system reduces effectively vibrations in the panel, which are transmitted through support structures of the five actuators and excited by emitted sound wave from the ceiling surface of concrete slab structure. The system works as the robust feedback control system for rejecting the disturbance in the panel detected with the acceleration sensors. The result of the control experiment proved the effectiveness of the control system showing 6 [dB] reductions of the acceleration in the major vibration modes of the plate.
In recent years, not only ruggedness but also neutrality has been recognized as an important feature of a fitness landscape for artificial genetic search. In this paper, we propose the use of the Nei's standard genetic distance, which was originally proposed in population genetics, for estimating the degree of neutrality in fitness landscapes. The characteristics of the Nei's standard genetic distance are shown by applying the standard genetic distance to artificial evolution for tunably neutral NK fitness landscapes. Further investigations are conducted in a complex evolutionary robotics fitness landscape to validate the proposed method. The results show that neural network controllers changing the number of hidden neurons have different levels of neutrality as well as ruggedness in their landscapes. This suggests to us that the Nei's standard genetic distance in natural evolution can be successfully applied to estimating the degree of neutrality in artificial evolution after minor modifications.
In this paper, exponential stability for neutral time-delay systems is discussed. First a sufficient condition is driven by using the characteristic equation, which is corresponding to the small gain theorem in the input-output stability theory. Based on this condition, an LMI stability condition is given by estimating the bound of L∞ norm of the time-delay element using the Padé approximants. The condition can also be applied to retarded time-delay systems in a special case. Numerical examples illustrate that when the time-delay is relatively short the obtained condition is less conservative than previous LMI ones led from the Lyapunov stability theory.