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Zbl 0826.93028
Apkarian, Pierre; Gahinet, Pascal
A convex characterization of gain-scheduled ${\cal H}\sb \infty$ controllers. (English)
[J] IEEE Trans. Autom. Control 40, No.5, 853-864 (1995). ISSN 0018-9286

Summary: An important class of linear time-varying systems consists of plants where the state-space matrices are fixed functions of some time-varying physical parameters $\theta$. Small gain techniques can be applied to such systems to derive robust time-invariant controllers. Yet, this approach is often overly conservative when the parameters $\theta$ undergo large variations during system operation. In general, higher performance can be achieved by control laws that incorporate available measurements of $\theta$ and therefore ``adjust'' to the current plant dynamics. This paper discusses extensions of ${\cal H}_\infty$ synthesis techniques to allow for controller dependence on time-varying but measured parameters. When this dependence is linear fractional, the existence of such gain-scheduled ${\cal H}_\infty$ controllers is fully characterized in terms of linear matrix inequalities. The underlying synthesis problem is therefore a convex program for which efficient optimization techniques are available. The formalism and derivation techniques developed here apply to both the continuous- and discrete-time problems. Existence conditions for robust time-invariant controllers are recovered as a special case, and extensions to gain- scheduling considering parametric uncertainty are discussed. In particular, simple heuristics are proposed to compute such controllers.

MSC 2000:: *93B36 $H^\infty$-control
93B50 Synthesis problems
93C25 Control systems in abstract spaces
93B51 Design techniques in systems theory
93B35 Sensitivity (robustness) of control systems

Keywords: linear; time-varying; robust; ${\cal H}\sb \infty$ synthesis; gain- scheduled; linear matrix inequalities; convex program

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Zentralblatt MATH Berlin [Germany]