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Gain-scheduled ℋ2 and ℋ∞ control of discrete-time polytopic time-varying systems

Gain-scheduled ℋ2 and ℋ∞ control of discrete-time polytopic time-varying systems

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This study presents ℋ2 and ℋ∞ performance analysis and synthesis procedures for the design of both gain-scheduled and robust static output feedback controllers for discrete-time linear systems with time-varying parameters. The obtained controllers guarantee an upper bound on the ℋ2 or ℋ∞ performance of the closed-loop system. As an immediate extension, the mixed ℋ2/ℋ∞ guaranteed cost control problem is also addressed. The scheduling parameters vary inside a polytope and are assumed to be a priori unknown, but measured in real-time. If bounds on the rate of parameter variation are known, they can be taken into account, providing less conservative results. The geometric properties of the polytopic domain are exploited to derive finite sets of linear matrix inequalities (LMIs) based on the existence of a parameter-dependent Lyapunov function. An application of the methodology to a realistic vibroacoustic problem, with experimentally obtained data, illustrates the benefits of the proposed approach and shows that the techniques can be used for real engineering problems.

Inspec keywords: H∞ control; time-varying systems; discrete time systems; closed loop systems; Lyapunov methods; linear systems; robust control; feedback; linear matrix inequalities

Other keywords: discrete polytopic time varying systems; gain-scheduled controllers; discrete time linear systems; polytopic domain; performance analysis; robust static output feedback controllers; closed loop system; Lyapunov function; linear matrix inequalities; vibroacoustic problem; H infinity control

Subjects: Stability in control theory; Time-varying control systems; Linear algebra (numerical analysis); Discrete control systems; Optimal control

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