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Local stabilization for linear discrete-time systems with bounded controls and norm-bounded time-varying uncertainty. (English) Zbl 0926.93054

The paper addresses the problem of locally stabilizing a linear discrete-time system subject to input constraints and affected by uncertainties in its matrices of the norm bounded time-varying type. The class of controls considered is the one consisting of saturated state feedback control laws. The required control gain matrix and a robust stability domain are obtained solving a certain discrete Riccati equation. The authors state sufficient conditions such that the problem has a solution. The control problem is translated into LMI conditions and moreover connections between local stability results and disturbance rejection problem are stated. Finally, an example is offered to illustrate the results and some interesting extensions of the approach are given.

MSC:

93D15 Stabilization of systems by feedback
93C55 Discrete-time control/observation systems
15A39 Linear inequalities of matrices
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