Nonlinear \(H_\infty\) output feedback control with integrator for polynomial discrete-time systems. (English) Zbl 1312.93039
Summary: This paper investigates the problem of designing a nonlinear \(H_\infty\) output feedback controller for a class of polynomial discrete-time systems. In general, this problem is hard to be formulated in a convex form because the relation between the control input and the Lyapunov function is always not jointly convex. Therefore, the problem cannot be solved via SemiDefinite Programming (SDP). On the basis of the Sum Of Squares (SOS) approach and incorporation of an integrator into the controller, sufficient conditions for the existence of a nonlinear \(H_\infty\) output feedback controller are given in terms of SOS conditions, which can be solved by an SDP solver. In contrast to the existing methods, a less conservative result is obtained. Finally, numerical examples are used to demonstrate the validity of this integrator approach.
MSC:
| 93B36 | \(H^\infty\)-control |
| 93B52 | Feedback control |
| 93C10 | Nonlinear systems in control theory |
| 93C55 | Discrete-time control/observation systems |
| 90C22 | Semidefinite programming |
Keywords:
\(H_\infty\) output feedback control; integrator approach; polynomial discrete-time systems; sum of squares decomposition; semidefinite programming (SDP)References:
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