Abstract
The issue of the exponential stability of interfered discrete-time delayed systems with saturation is considered in this paper. The state saturation is constrained by a convex hull, allowing for the application of a suitable Lyapunov–Krasovskii functional to derive an exponential stability criterion. Improved summation inequalities are used to manage the sum terms in the forward difference of the Lyapunov–Krasovskii functional. The results can be used to assure the nonexistence of limit cycles in the system. Compared to previous methods, the present method leads to improved results. Two examples are given to highlight the importance of the obtained results.
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Abbreviations
- 0 :
-
Null vector or null matrix
- I :
-
Identity matrix
- \({\mathbb{R}}^{\kappa }\) :
-
\(\kappa\)-Dimensional Euclidean space
- \({\mathbb{R}}^{\kappa \times \mu }\) :
-
Set of \(\kappa \times \mu\) real matrices
- \({\varvec{C}}^{{\text{T}}}\) :
-
Transpose of \({\varvec{C}}\)
- \({\varvec{C}} > {\mathbf{0}}\;\left( { \ge {\mathbf{0}}} \right)\) :
-
\({\varvec{C}}\) is a symmetric positive-definite (semidefinite) matrix
- \({\varvec{C}} < {\mathbf{0}}\) :
-
\({\varvec{C}}\) is a symmetric negative-definite matrix
- \(\left\| \cdot \right\|_{\infty }\) :
-
Infinity norm
- \(\lambda_{{\text{max}}} \left( {\varvec{C}} \right)\) :
-
Maximum eigenvalue of the matrix \({\varvec{C}}\)
- \(\lambda_{{\text{min}}} \left( {\varvec{C}} \right)\) :
-
Minimum eigenvalue of the matrix \({\varvec{C}}\)
- \(*\) :
-
Symmetric entries in a symmetric matrix
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Kanithi, S.K.M., Kandanvli, V.K.R. & Kar, H. Limit Cycle-Free Realization of Interfered Discrete-Time Systems with Time-Varying Delay and Saturation. J Control Autom Electr Syst (2024). https://doi.org/10.1007/s40313-024-01074-0
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DOI: https://doi.org/10.1007/s40313-024-01074-0