Graph-Based Minimum Dwell Time and Average Dwell Time Computations for Discrete-Time Switched Linear Systems
For control theorists working on stability of switched systems, this work provides a computational framework extending existing graph-based methods to handle defective matrices and improve dwell time estimates.
The paper presents graph-based methods to compute the minimum and average dwell times ensuring asymptotic stability for discrete-time switched linear systems with switching governed by a digraph, using maximum cycle ratio and mean calculations on doubly weighted digraphs. The approach handles defective subsystem matrices via Jordan decomposition and improves estimates for bimodal systems through scaling algorithms.
Discrete-time switched linear systems where switchings are governed by a digraph are considered. The minimum (or average) dwell time that guarantees the asymptotic stability can be computed by calculating the maximum cycle ratio (or maximum cycle mean) of a doubly weighted digraph where weights depend on the eigenvalues and eigenvectors of subsystem matrices. The graph-based method is applied to systems with defective subsystem matrices using Jordan decomposition. In the case of bimodal switched systems scaling algorithms that minimizes the condition number can be used to give a better minimum (or average) dwell time estimates.