Stability for time varying linear dynamic systems on time scales

By Jeffrey J. Dacunha. 2005

205 citations recorded by the source corpus.

We study conditions under which the solutions of a time varying linear dynamic system of the form xΔ(t)=A(t)x(t) are stable on certain time scales. We give sufficient conditions for various types of stability, including Lyapunov-type stability criteria and eigenvalue conditions on "slowly varying" systems that ensure exponential stability. Finally, perturbations of the unforced system are investigated, and an instability criterion is also developed.

Subfields: Applied Mathematics, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/1e1e0dd62d4905599b886ebad87a559d044773ff

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. John M. Davis
2. Shimon Whiteson
3. Bo Liu
4. Billy Jackson
5. Shangtong Zhang
6. Hengshuai Yao
7. Douglas R. Anderson

In Control and Systems Engineering

1. John M. Davis
2. Shimon Whiteson
3. Bo Liu
4. Shangtong Zhang
5. Hengshuai Yao

Citations in the corpus

• CONTROLLABILITY, OBSERVABILITY, REALIZABILITY, AND STABILITY OF DYNAMIC LINEAR SYSTEMS (2009, background): “DaCunha also deals with this concept under a different definition in [10, 11] and emphasizes the time varying case.”
• Linear impulsive dynamic systems on time scales (2010, unknown): “We refer to the books [9], [15], [16], [32] and the papers [1], [3], [17], [20], [21], [24], [30], [34], [38], [40], [41].”
• Provably Convergent Off-Policy Actor-Critic with Function Approximation (2019, methodology): “It is usually hard to employ a Lyapunov approach to establish the boundedness of such time-varying linear systems (e.g., see DaCunha (2005)).”