In this paper, we treat 2 dimensional systems or systems which can be approximated as 2 dimensional systems. We will propose a PI control scheme of a servo system design that gives the shortest M% settling time and satisfies a percent overshoot requirement for an assigned M. The usefulness of the proposing method is demonstrated through examples.

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This research is concerned with a bifurcation analysis of a stochastic predator-prey system. The P-bifurcation (Phenomenological bifurcation) and the D-bifurcation (Dynamical bifurcation) are major analytical methods for the stochastic bifurcation. The P-bifurcation studies a stationary measure corresponding to the one-point motion, while the D-bifurcation approach is based on the stability of invariant measures. Since the P-bifurcation is based on the one point-motion, there is a possibility to miss certain branches in bifurcation. So, we study the bifurcation of the stochastic predator-prey system with help of the D-bifurcation, and analyze the influence of the random noise on the bifurcation phenomena in the proposed stochastic model.

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This paper considers circle fitting problems by an averaging consensus algorithm of multi-agent systems. We propose a distributed approach where each agent arranged in a plane estimates a circle that minimizes the algebraic or geometric distance to all agents. The simulation result shows that the proposed circle fitting can find the optimal circle by the distributed consensus algorithm.

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This paper addresses the design problem of fixed-structure dynamic quantizers for discrete-valued input control. The problem is to find a dynamic quantizer when the dimension and the decentralized structure of quantizer are given as design specifications. In this paper, we first formulate a quantizer design problem under constraint conditions such as stability and input saturation. Then, for getting a solution to the problem, we provide a simple and useful design method with a particle swarm optimization which is one of evolutionary algorithms. Finally, we verify that the proposed method gives satisfactory fixed-structure dynamic quantizers, by several numerical examples.

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