Finite-time stability and \(H_{\infty}\) control of linear discrete-time delay systems with norm-bounded disturbances. (English) Zbl 1344.93043
Summary: This paper deals with the finite-time stability and \(H_{\infty}\) control of linear discrete-time delay systems. The system under consideration is subject to interval time-varying delay and norm-bounded disturbances. Linear matrix inequality approach is used to solve the finite-time stability problem. First, new sufficient conditions are established for robust finite-time stability of the linear discrete-time delay system with norm-bounded disturbances, then the state feedback controller is designed to robustly finite-time stabilize the system and guarantee an adequate level of system performance. The delay-dependent sufficient conditions are formulated in terms of Linear Matrix Inequalities (LMIs). Numerical examples are given to illustrate the effectiveness of the proposed results.
MSC:
| 93B36 | \(H^\infty\)-control |
| 93C55 | Discrete-time control/observation systems |
| 93C05 | Linear systems in control theory |
| 93D09 | Robust stability |
| 93B52 | Feedback control |
Keywords:
finite-time stability; \(H_{\infty}\) control; time-varying delay; disturbances; linear matrix inequalitiesReferences:
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