Solution to the Common Lyapunov-Function Problem via Fusion of Numerical and thalytical Aspec

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1. We first tested several methods available to solve LMI,into which the common Lyapunov function problem can be recast, and found the so-called interior-point method most suitable for the present purpose. Based on this method, we developed a computation code by ourselves and used it throughout the study.2. With knowledge or experience attained in the above computation process, we are successful in finding some subclasses of systems, continuous-time or discrete-time, that have a quadratic Lyapunov function in common. Some subclasses for low-order systems have also been found. In general, we noticed, there exists a parallel between continuous-time case and discrete-time one. This would give a further insight into the problem.3. Since there exists a close connection between the problem in question and the quadratic stability problem of systems, we looked into the quadratic stability property of interval polynomials and obtained some results.