Robust Nonlinear H ∞ State Feedback Control of Polynomial Discrete-Time Systems: An Integrator Approach
This paper investigates the problem of designing a nonlinear H ∞ state feedback controller for polynomial discrete-time systems with norm-bounded uncertainties. In general, the problem of designing a controller for polynomial discrete-time systems is difficult, because it is a nonconvex problem. Mor...
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Springer US
2013
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| Online Access: | http://eprints.utem.edu.my/id/eprint/11076/1/s00034-013-9645-9 http://eprints.utem.edu.my/id/eprint/11076/ http://link.springer.com/journal/34 |
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| author | Md Saat, Mohd Shakir |
| author_facet | Md Saat, Mohd Shakir |
| author_sort | Md Saat, Mohd Shakir |
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| content_provider | Universiti Teknikal Malaysia Melaka |
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| continent | Asia |
| country | Malaysia |
| description | This paper investigates the problem of designing a nonlinear H ∞ state feedback controller for polynomial discrete-time systems with norm-bounded uncertainties. In general, the problem of designing a controller for polynomial discrete-time systems is difficult, because it is a nonconvex problem. More precisely, in general, its Lyapunov function and control input are not jointly convex. Hence, it cannot be solved by semidefinite programming. In this paper, a novel approach is proposed, where an integrator is incorporated into the controller structure. In doing so, a convex formulation of the controller design problem can be rendered in a less conservative way than the available approaches. Furthermore, we establish the interconnection between robust H ∞ control of polynomial discrete-time systems with norm-bounded uncertainties and H ∞ control of scaled polynomial discrete-time systems. This establishment allows us to convert the robust H ∞ control problems to H ∞ control problems. Then, based on the sum of squares (SOS) approach, sufficient conditions for the existence of a nonlinear H ∞ state feedback controller are given in terms of solvability of polynomial matrix inequalities (PMIs), which can be solved by the recently developed SOS solvers. A tunnel diode circuit is used to demonstrate the validity of this integrator approach |
| format | Article |
| id | my.utem.eprints-11076 |
| institution | Universiti Teknikal Malaysia Melaka |
| language | en |
| publishDate | 2013 |
| publisher | Springer US |
| record_format | eprints |
| spelling | my.utem.eprints-110762015-05-28T04:15:12Z http://eprints.utem.edu.my/id/eprint/11076/ Robust Nonlinear H ∞ State Feedback Control of Polynomial Discrete-Time Systems: An Integrator Approach Md Saat, Mohd Shakir TK Electrical engineering. Electronics Nuclear engineering This paper investigates the problem of designing a nonlinear H ∞ state feedback controller for polynomial discrete-time systems with norm-bounded uncertainties. In general, the problem of designing a controller for polynomial discrete-time systems is difficult, because it is a nonconvex problem. More precisely, in general, its Lyapunov function and control input are not jointly convex. Hence, it cannot be solved by semidefinite programming. In this paper, a novel approach is proposed, where an integrator is incorporated into the controller structure. In doing so, a convex formulation of the controller design problem can be rendered in a less conservative way than the available approaches. Furthermore, we establish the interconnection between robust H ∞ control of polynomial discrete-time systems with norm-bounded uncertainties and H ∞ control of scaled polynomial discrete-time systems. This establishment allows us to convert the robust H ∞ control problems to H ∞ control problems. Then, based on the sum of squares (SOS) approach, sufficient conditions for the existence of a nonlinear H ∞ state feedback controller are given in terms of solvability of polynomial matrix inequalities (PMIs), which can be solved by the recently developed SOS solvers. A tunnel diode circuit is used to demonstrate the validity of this integrator approach Springer US 2013 Article PeerReviewed text/plain en http://eprints.utem.edu.my/id/eprint/11076/1/s00034-013-9645-9 Md Saat, Mohd Shakir (2013) Robust Nonlinear H ∞ State Feedback Control of Polynomial Discrete-Time Systems: An Integrator Approach. Circuits, Systems, and Signal Processing, Volume 33 (2). pp. 331-346. ISSN 1531-5878 http://link.springer.com/journal/34 |
| spellingShingle | TK Electrical engineering. Electronics Nuclear engineering Md Saat, Mohd Shakir Robust Nonlinear H ∞ State Feedback Control of Polynomial Discrete-Time Systems: An Integrator Approach |
| title | Robust Nonlinear H ∞ State Feedback Control of Polynomial Discrete-Time Systems: An Integrator Approach |
| title_full | Robust Nonlinear H ∞ State Feedback Control of Polynomial Discrete-Time Systems: An Integrator Approach |
| title_fullStr | Robust Nonlinear H ∞ State Feedback Control of Polynomial Discrete-Time Systems: An Integrator Approach |
| title_full_unstemmed | Robust Nonlinear H ∞ State Feedback Control of Polynomial Discrete-Time Systems: An Integrator Approach |
| title_short | Robust Nonlinear H ∞ State Feedback Control of Polynomial Discrete-Time Systems: An Integrator Approach |
| title_sort | robust nonlinear h ∞ state feedback control of polynomial discrete-time systems: an integrator approach |
| topic | TK Electrical engineering. Electronics Nuclear engineering |
| url | http://eprints.utem.edu.my/id/eprint/11076/1/s00034-013-9645-9 http://eprints.utem.edu.my/id/eprint/11076/ http://link.springer.com/journal/34 |
| url_provider | http://eprints.utem.edu.my/ |