Macau, ChinaOn the asymptotic stability of 2-D linear inhomogeneous systems
Published in IEEE Transactions on Automatic Control, 2025
Recommended citation: Y. Ju, J. Reis, Y. Sun, and C. Silvestre, “On the asymptotic stability of 2-D linear inhomogeneous systems,” Transactions on Automatic Control, IEEE, (in press), 2025.
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Abstract
In this technical note, we investigate the stability of discrete-time two-dimensional (2-D) linear inhomogeneous systems. Specifically, we establish sufficient conditions that guarantee both asymptotic and exponential stability. Compared to existing results, the conditions presented here relax the requirement for the negative definiteness of differences in (piecewise) Lyapunov functions, allowing these functions to grow over certain periods. Numerical examples are provided to illustrate the theoretical findings.