When a mathematical model is not available for a dynamical system, it is reasonable to use a data-driven approach for analysis and control of the system. With this motivation, the authors have recently developed a data-driven solution to Lyapunov equations, which uses not the model but the data of several state trajectories of the system. However, the number of state trajectories to uniquely determine the solution is O(n2) for the dimension n of the system. This prevents us from applying the method to a case with a large n. Thus, this paper proposes a novel class of data-driven Lyapunov equations, which requires a smaller amount of data. Although the previous method constructs one scalar equation from one state trajectory, the proposed method constructs three scalar equations from any combination of two state trajectories. Based on this idea, we derive data-driven Lyapunov equations such that the number of state trajectories to uniquely determine the solution is O(n).

The main purpose of Codemark is to distribute digital contents using offline media. Due to the main purpose of Codemark, Codemark cannot be used on digital images. It has high robustness on only printed images. This paper presents a new color code called Robust Index Code (RIC for short), which has high robustness on JPEG Compression and Resize targeting digital images. RIC embeds a remote database index to digital images so that users can reach to any digital contents. Experimental results, using our implemented RIC encoder and decoder, have shown high robustness on JPEG Comp. and Resize of the proposed codemark. The embedded database indexes can be extracted 100% on compressed images to 30%. In conclusion, it is able to store all the type of digital products by embedding indexes into digital images to access database, which means it makes a Superdistribution system with digital images realized. Therefore RIC has the potential for new Internet image services, since all the images encoded by RIC are possible to access original products anywhere.

A method for the exact cost performance analysis of autonomous discrete-time piecewise affine systems is presented. Cost performance refers to the average trajectory cost over the entire region of attraction of the origin. The trajectory cost is based on the infinite-horizon cost. First, a reverse reachability algorithm which constructs the explicit piecewise quadratic trajectory cost function over the entire region of attraction of the origin is presented. Then, an explicit expression for the integral of a quadratic function over a simplex of arbitrary dimension is derived. Thus, the piecewise quadratic trajectory cost function can be integrated exactly and efficiently in order to determine the cost performance of the system as a whole. This alleviates the need to perform a large number of simulations.

This paper proposes a notion of a controllability measure of discrete-time piecewise affine systems, which is a natural extension of the controllability gramian of linear systems. Although this measure is calculated in a probabilistic way, it may be applied to control of biological systems for providing a policy to experiments for pharmaceutical developments. Thus an application to gene regulatory control of luminescence in the marine bacterium modeled by the piecewise affine system is discussed in this paper.