GRAPHS, CAUSALITY, AND STABILIZABILITY - LINEAR, SHIFT-INVARIANT SYSTEMS ON L2[0,INFINITY]

被引：54

作者：

GEORGIOU, TT ^{[1
]}

SMITH, MC ^{[1
]}

机构：

[1] UNIV CAMBRIDGE, DEPT ENGN, CAMBRIDGE CB2 1PZ, ENGLAND

来源：

MATHEMATICS OF CONTROL SIGNALS AND SYSTEMS | 1993年 / 6卷 / 03期

关键词：

SYSTEM THEORY; LINEAR GRAPHS; TIME-INVARIANCE; STABILIZABILITY; CAUSALITY; CAUSAL EXTENDIBILITY; W-STABILITY;

D O I：

10.1007/BF01211620

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

This paper presents a number of basic elements for a system theory of linear, shift-invariant systems on L2[0, infinity). The framework is developed from first principles and considers a linear system to be a linear (possibly unbounded) operator on L2[0, infinity). The properties of causality and stabilizability are studied in detail, and necessary and sufficient conditions for each are obtained. The idea of causal extendibility is discussed and related to operators defined on extended spaces. Conditions for w-stabilizability and w-stability are presented. The graph of the system (operator) plays a unifying role in the definitions and results. We discuss the natural partial order on graphs (viewed as subspaces) and its relevance to systems theory.

引用

页码：195 / 223

页数：29

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