On strong structural controllability and observability of linear time-varying systems: a constructive method

Abstract

In this paper, we consider the controllability and observability of generalized linear time-varying (LTV) systems whose coefficients are not exactly known. All that is known about these systems is the placement of non-zero entries in their coefficient matrices (A, B). We provide the characterizations in order to judge whether the placements can guarantee the controllability/observability of such LTV systems, regardless of the exact value of each non-zero coefficient. We also present a direct and efficient algorithm with an associated time cost of O(n + m + ν) to verify the conditions of our characterizations, where n and m denote the number of columns of A and B, respectively, and ν is number of non-zero entries in (A, B).

Structural controllability of networked systems with general heterogeneous subsystems

“…According to Example 1, to achieve structural controllability of the simplified chain-networked system (10), it's necessary that q i ≤ q i−1 , i = 2, … , N. Corollary 4. A chain-networked system (10) with minimum q i is structurally controllable, if and only if q 1 ≥ q 2 ≥ … ≥ q N with |M * w i,i−1 | = q i , i = 2, … , N. Since q i may be not unique, the following condition is a sufficient condition.…”

“…In recent years, structural controllability of linear systems and complex networks has been widely studied from algebraic and graphical perspectives, and some efficient criteria have been established, where most, if not all, results on the structural controllability are derived under the assumption that the dimension of the state of each node is one, i.e., the dynamics in the nodes are hidden [3][4][5][6][7][8][9][10][11].…”

Resilience Analysis of Discrete-Time Networked System in the Presence of Information Disclosure

“…In the later discussion, we will show that the analysis of observing global information for the proposed eavesdropping model is related to the observability of traditional linear systems. Till now, there have been extensive studies on the observability of high-dimensional linear systems [23]- [27]. In view of the dual nature of controllability and observability, one can refer to the research on the controllability of complex networks.…”