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| Titel: |
Robust stability and stabilization of discrete-time non-linear systems: the LMI approach |
| Auteur: |
Stipanovic, D. M. Siljak, D. D. |
| Verschenen in: |
International journal of control |
| Paginering: | Jaargang 74 (2001) nr. 9 pagina's 873-879 |
| Jaar: |
2001-06-15 |
| Inhoud: |
The purpose of this paper is to convert the problem of robust stability of a discrete-time system under non-linear perturbation to a constrained convex optimization problem involving linear matrix inequalities (LMI). The nominal system is linear and time-invariant, while the perturbation is an uncertain non-linear time-varying function which satisfies a quadratic constraint. We show how the proposed LMI framework can be used to select a quadratic Lyapunov function which allows for the least restrictive non-linear constraints. When the nominal system is unstable the framework can be used to design a linear state feedback which stabilizes the system with the same maximal results regarding the class of non-linear perturbations. Of particular interest in this context is our ability to use the LMI formulation for stabilization of interconnected systems composed of linear subsystems with uncertain non-linear and time-varying coupling. By assuming stabilizability of the subsystems we can produce local control laws under decentralized information structure constraints dictated by the subsystems. Again, the stabilizing feedback laws produce a closed-loop system that is maximally robust with respect to the size of the uncertain interconnection terms. |
| Uitgever: |
Taylor & Francis |
| Bronbestand: |
Elektronische Wetenschappelijke Tijdschriften |
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