Research Initiation Award: Further Development of a UnifiedLinear System Theory and its Applications in Control and Communication Systems

众所周知，自研究微分方程组以来，时变线性(TVL)和非线性(TVNL)动力系统的分析一直是一个难以解决的数学问题。因此，具有时变参数的控制、通信和信号处理系统很难处理。最近(1987-1989)，对于这类标量TVL系统，建立了一个新的统一的线性系统理论(ULST)。在此理论的基础上，发展了一种新的镇定控制技术，称为扩展平均分配(EMA)控制，用于TVL和TVNL动态系统(1990)。这一新的理论和控制技术正受到控制和系统界越来越多的关注，并在航空航天、制造和国防工业中发现了潜在的应用。本研究项目的目的是将这些结果推广到更一般的多输入多输出(MIMO)TVL系统x=A(T)+B(T)u，并促进ULST和EMA控制技术在控制、通信和信号处理方面的工业应用。这项拟议的研究将采用微分-代数方法。预期的研究结果将建立一般类型的TVL动力系统(微分方程)x=A(T)x+B(T)u的谱特征、精确的稳定性判据和求解技术，这将使科学家/工程师能够有效地处理原本难以解决的科学/工程问题。相信这些研究领域的成果将是现代系统科学和控制工程的革命性突破。

It is well known that the analysis of Time-Varying Linear (TVL) and Nonlinear (TVNL) dynamical systems has been an elusive mathematical problem since the beginning of the studies of differential equations. Consequently, control, communication and signal processing systems with time-varying parameters are difficult to deal with. Recently (1987-1989) a new and Unified Linear System Theory (ULST) has been established for the class of scalar TVL systems of the form. Based on the theory, a novel stabilization control technique, called Extended-Mean Assignment (EMA) control, for TVL and TVNL dynamical systems has been developed (1990). The new theory and control technique is gaining an increasing interest in the control and systems community, and has found potential applications in aerospace, manufacturing and defense industries. The goals of this research project is to extend those results to the more general class of Multi-Input-Multi-Output (MIMO) TVL system x = A(t)+B(t)u; and to promote industrial applications of the ULST and EMA control technique in control, communications and signal processing. The proposed research will employ a differential-algebraic approach. The anticipated research results will establish a spectral characterization, precise stability criteria and solution techniques for the general class of TVL dynamical systems (differential equations) x = A(t)x+B(t)u, which will enable scientists/engineers to effectively deal with otherwise intractable scientific/engineering problems. It is believed that achievements in the proposed research areas will constitute a revolutionary breakthrough in modern systems science and control engineering.