Abstract
An equivalent linear matrix inequality (LMI) representation of bounded real lemma (BRL) for linear continuous-time systems is introduced. As to LTI system including polytopic-type uncertainties, by using a parameter-dependent Lyapunov function, there are several LMIs-based formulations for the analysis and synthesis of performance. All of these representations only provide us with different sufficient conditions. Compared with previous methods, this new representation proposed here provides us the possibility to obtain better results. Finally, some numerical examples are illustrated to show the effectiveness of proposed method.
Highlights
In the past two decades, H∞ theory is one of the most sophisticated frameworks for robust control system design
Based on bounded real lemma BRL, H∞ norm computation problem can be transferred into a standard linear matrix inequality optimization formulation, which includes the product of the Lyapunov function matrix and system matrices
By using parameter-dependent Lyapunov function, this representation can reduce the conservatism that occurs in the analysis and synthesis problems of linear systems with polytopic-type uncertainties
Summary
In the past two decades, H∞ theory is one of the most sophisticated frameworks for robust control system design. In 11, 12 , simple modifications of bounded real lemma are introduced for the analysis and the design of continuous-time system with polytopic-type uncertainty; the results still are somewhat conservative. De Oliveira et al presented some sufficient LMI-based conditions to compute H∞ guaranteed costs for linear time-invariant systems with polytopic-type uncertainties 13 , the controller design problem has not been considered yet. By using parameter-dependent Lyapunov function, this representation can reduce the conservatism that occurs in the analysis and synthesis problems of linear systems with polytopic-type uncertainties. Thereby, based on this representation, robust state feedback synthesis problem is solved with less conservatism than other methods from literature. The solution to H∞ state feedback control of a satellite system with a polytopic uncertainty is considered in the second example just as in 11
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