Showing papers by "Eric Chu published in 2007"

Projected Generalized Discrete-Time Periodic Lyapunov Equations and Balanced Realization of Periodic Descriptor Systems

Abstract: From the necessary and sufficient conditions for complete reachability and observability of periodic descriptor systems with time-varying dimensions, the symmetric positive semidefinite reachability/observability Gramians are defined. These Gramians can be shown to satisfy some projected generalized discrete-time periodic Lyapunov equations. We propose a numerical method for solving these projected Lyapunov equations, and give an illustrative numerical example. As an application of our results, the balanced realization of periodic descriptor systems is discussed.

A Near-optimal Solution for the Heterogeneous Multi-processor Single-level Voltage Setup Problem

Abstract: A heterogeneous multi-processor (HeMP) system consists of several heterogeneous processors, each of which is specially designed to deliver the best energy-saving performance for a particular category of applications. A low-power real-time scheduling algorithm is required to schedule tasks on such a system to minimize its energy consumption and complete all tasks by their deadline. The problem of determining the optimal speed for each processor to minimize the total energy consumption is called the voltage setup problem. This paper provides a near-optimal solution for the HeMP single-level voltage setup problem. To our best knowledge, we are the first work that addresses this problem. Initially, each task is assigned to a processor in a local-optimal manner. We next propose a couple of solutions to reduce energy by migrating tasks between processors. Finally, we determine each processor's speed by its final workload and the deadline. We conducted a series of simulations to evaluate our algorithms. The results show that the local-optimal partition leads to a considerably better energy-saving schedule than a commonly-used homogeneous multi-processor scheduling algorithm. Furthermore, at all measurable configurations, our energy consumption is at most 3% more than the optimal value obtained by an exhaustive iteration of all possible task-to-processor assignments. In summary, our work is shown to provide a near-optimal solution at its polynomial-time complexity.

A schur-newton algorithm for robust pole assignment

Abstract: We propose an algorithm for the state feedback pole assignment problem. The algorithm is the first of its kind, making use of the Schur form and minimizing the departure from normality of the closed-loop poles by Newton’s method. Eleven illustrative examples, comparing our algorithm with three other existing ones, are given.