Robust regulation of discrete-time systems subject to parameter uncertainties and state delay. (English) Zbl 1520.93293
Summary: This paper deals with the robust recursive regulation problem of uncertain discrete-time linear systems subject to unknown state delays. The variation rate between two consecutive delays is considered bounded. The parameter matrices are affected by norm-bounded uncertainties. Applying the lifting method and modeling the delay as a Markov chain, systems with state delays are converted to augmented delay-free Markovian jump linear systems. Then, a robust recursive linear quadratic regulator is obtained, solving an optimization problem through robust regularized least-squares approaches. The solution is given in terms of algebraic Riccati equations. We assess the proposed regulator through a numerical example and compare its performance with other robust control approaches.
MSC:
| 93C55 | Discrete-time control/observation systems |
| 93C05 | Linear systems in control theory |
| 49N10 | Linear-quadratic optimal control problems |
| 93C43 | Delay control/observation systems |
| 93E03 | Stochastic systems in control theory (general) |
Keywords:
time-delay system; discrete-time linear system; Markovian jump linear system; robust linear quadratic regulatorReferences:
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