Abstract
In previous work the stabilization of Orthogonal Piecewise Linear (OPL) systems was considered and a simple design technique was outlined. In this paper the problems of robustness analysis and design for OPL systems are investigated. It is shown that, due to simplicity in the algebra involved, piecewise-linear Lyapunov functions offer considerable ease in addressing robustness. Assuming real structured parametric uncertainties in general affine linear state-space models, time-varying or state-dependent uncertainties as well as modeling errors can be taken into account, while retaining the same spirit in the design procedure. Bounds for the uncertain parameters can be easily found using linear programming and the computational complexity is kept low. These issues complete the OPL framework and confirm that it constitutes a simple design technique for addressing stability, performance and robustness while taking into account control limitations.
This research was supported by the EPSRC under grant GR/K 36300 and studentship Ref. No. 97700206 for the first author. The support of the UMIST graduate research fund is also acknowledged.
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References
Blanchini, F.: Nonquadratic Lyapunov functions for Robust Control. Automatica 31(3) (1995) 451–461
Branicky, M.: Multiple Lyapunov functions and Other Analysis Tools for Switched and Hybrid Systems. IEEE Trans. Automatic Control 43(4) (1998) 475–482
Gardiner, J.: Computation of Stability Robustness Bounds for State-Space Models with Structured Uncertainty. IEEE Trans. Automatic Control 42(2) (1997) 253–256
McConley, M.W., Dahleh, M.A., Feron E.: Polytopic Control Lyapunov Functions for Robust Stabilization of a Class of Nonlinear Systems. In Proc. ACC’97 416–419
Johansson, M., Rantzer A.: Computation of Piecewise Quadratic Lyapunov functions for Hybrid Systems. IEEE Trans. Automatic Control 43(4) (1998) 555–559
Kiendl, H., Ruger J.J.: Stability analysis of fuzzy control systems using facet functions. Fuzzy sets and systems 70 (1995) 275–285
Pettit, N.B.O.L., Muir A.: Simple control of nonlinear systems. In Proc. ECC'’97
Song, G., Mukherjee R.: A comparative study of Conventional Nonsmooth Time-Invariant and Smooth Time-Varying Robust compensators. IEEE Trans. Control Systems Technology 6:4 (1998) 571–576
Tanaka, K., Ikeda T., Wang H.O.: Robust stabilization of a class of uncertain nonlinear systems via fuzzy control: Quadratic stabilizability, H∞control theory and linear matrix inequalities. IEEE Trans. Fuzzy systems 4:1 (1996) 1–13
Yfoulis, C.A., Muir, A., Pettit, N.B.O.L., Wellstead, P.E.: Stabilization of Orthogonal Piecewise Linear systems using Piecewise-Linear Lyapunov-like functions. Control Systems Centre Internal report 875 (1998). WWW home page: http://www.csc.umist.ac.uk
Yfoulis, C.A., Muir, A., Pettit, N.B.O.L., Wellstead, P.E.: Stabilization of Orthogonal Piecewise Linear systems using Piecewise-Linear Lyapunov-like functions. In Proc. CDC 98 (1998)
Zhou, K., Khargonekar, P.P.: Stability Robustness Bounds for Linear State-Space Models with Structured Uncertainty. IEEE Trans. Automatic Control 32(7) (1987) 621–623
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Yfoulis, C.A., Muir, A., Wellstead, P.E., Pettit, N.B.O.L. (1999). Stabilization of Orthogonal Piecewise Linear Systems: Robustness Analysis and Design. In: Vaandrager, F.W., van Schuppen, J.H. (eds) Hybrid Systems: Computation and Control. HSCC 1999. Lecture Notes in Computer Science, vol 1569. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48983-5_23
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DOI: https://doi.org/10.1007/3-540-48983-5_23
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