Robust H_∞ control for constrained discrete-time piecewise affine systems with time-varying parametric uncertainties

Author(s): Y. Gao ; Z. Liu ; H. Chen
DOI: 10.1049/iet-cta.2008.0182

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Author(s): Y. Gao ¹ ; Z. Liu ¹ ; H. Chen ²
- Affiliations: 1: Department of Control Science and Engineering, Harbin Institute of Technology, Harbin, People's Republic of China
  2: Department of Control Science and Engineering, Jilin University, Changchun, People's Republic of China
Source: Volume 3, Issue 8, August 2009, p. 1132 – 1144
DOI: 10.1049/iet-cta.2008.0182 , Print ISSN 1751-8644, Online ISSN 1751-8652

In this study, a novel robust H_∞ control scheme is presented for discrete-time piecewise affine (PWA) systems in the presence of time-varying uncertainties, external disturbance and time-domain constraints. The suggested control method is formulated as linear matrix inequalities (LMIs), and solved much more efficiently than current methods which could be only cast as bilinear matrix inequalities (BMIs). The key ideas are to introduce a parameter-dependent piecewise-quadratic Lyapunov function (PDPWQLF) to guarantee the closed-loop system to be energy dissipative, and use the concept of approximating polytopic operating regions by ellipsoids. The resulting controller can guarantee robust closed-loop properties, including stability, H_∞ performance and the satisfaction of constraints. An example is presented to verify the proposed theoretical results.

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Robust H∞ control for constrained discrete-time piecewise affine systems with time-varying parametric uncertainties

Robust H∞ control for constrained discrete-time piecewise affine systems with time-varying parametric uncertainties

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Robust H_∞ control for constrained discrete-time piecewise affine systems with time-varying parametric uncertainties

Robust H_∞ control for constrained discrete-time piecewise affine systems with time-varying parametric uncertainties