Abstract
The synthesis procedure of a control law that guarantees properties of robust stability with respect to structured parameter perturbations is proposed. The solution of the considered problem is based on the Razumikhin's method for functional differential equations generalized for parameter perturbation systems with time delay. The extension is obtained by using interval Lyapunov functions. The robust control law is represented through a solution of an interval matrix Riccati type equation.
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References
Andronov, A. A. and Pontryagin, L. S.: Robust System, Reports of Academy of Sciences of the USSR 14 (1937), pp. 356–359 (in Russian).
Bhattacharyya, S. P., Chapellat, H., and Keel, L. H.: Robust Control: The Parametric Approach, Prentice Hall PTR, Upper Saddle River, NJ, 1995.
Boyd, S. P., El Ghqoui, L., Feron, E., and Balakrishman, V.: Linear Matrix Inequalities in System and Control Theory, SIAM, Philadelphia, 1994.
Chang, S. S. L. and Peng, T. K. C.: Adaptive Guaranteed Cost Control of Systems with Uncertain Parameters, IEEE Trans. Autom. Control AC-17 (1972), pp. 474–483.
Dobronets, B. S. and Shaidurov, V. V.: Two-Side Numerical Methods, Novosibirsk, Nauka, 1990 (in Russian).
Douglas, J. and Alhans, M.: Robust Linear Quadratic Design with Real Parameter Uncertainty, IEEE Trans. Autom. Control AC-39 (1994), pp. 107–111.
Doyle, J. C., Glover, K., Khargonekar, P. P., and Francis, B. A.: State-Space Solution to Standard H 2 and H ∞ Control Problem, IEEE Trans. Autom. Control AC-34 (8) (1989), pp. 831–847.
Feron, E., Apkarian, P., and Gahinet, P.: Analysis and Synthesis of Robust Control System via Parameter-Dependent Lyapunov Function, IEEE Trans. Autom. Control AC-40 (1996), pp. 1041–1046.
Francis, B. A.: A Course in H ∞ Control Theory, Springer Verlag, 1987.
Francis, B. A. and Doyle, J. C.: Linear Control Theory with H∞ Optimality Criterion, SIAM J. Contr. Opt. 25 (1987), pp. 815–844.
Ikeda, M. and Ashida, T.: Stabilization of Linear Systems with Time Delay, IEEE Trans. Autom. Control 24 (1979), pp. 369–370.
Krasovkii, N. N.: Some Problems of Stable Theory of Motion, Nauka, Moscow, 1959 (in Russian).
Olas, A.: Construction of Optimal Lyapunov Function for System with Structured Uncertainties, IEEE Trans. Autom. Control AC-39 (1994), pp. 167–171.
Petersen, T. R. and Hollot, C. V.: Riccati Equation Approach to the Stabilization of Uncertain Linear Systems, Automatica 22 (1986), pp. 397–411.
Petersen, T. R. and McFarlane, D. C.: Optimal Guaranteed Cost Control and Filtering for Uncertain Linear Systems, IEEE Trans. Autom. Control AC-39 (1994), pp. 1971–1977.
Razumikhin, B. S.: Using Lyapunov Method to Some Problems of Stability of System with Time Delay, Automation and Telemechanics 21 (1960), pp. 740–748 (in Russian).
Sendov, B.: Some Topics of Segment Analysis, in: Nickel, K. (ed.), Interval Mathematics, Academic Press, New York, 1980, pp. 203–222.
Shary, S. P.: Outer Estimation of Generalized Solution Sets to Interval Linear Systems, Reliable Computing 5 (3) (1999), pp. 323–335.
Shashikhin, V. N.: Hierarchical Optimization of Large Scale Systems with Time Delay, Automation and Telemechanics 4 (1993), pp. 73–84 (in Russian).
Shashikhin, V. N.: Optimization of Nonlinear Systems by Using the Interval Linearization Method, International Journal of Computer and System Sciences 3 (1999), pp. 29–37.
Shashikhin, V. N.: Robust Stabilization of Interval Dynamic Systems, International Journal of Computer and Systems Sciences 6 (1996), pp. 47–53.
Weinhofer, J. K. and Haas, W. C.: H ∞ -Control Using Polynomial Matrices and Interval Arithmetic, Reliable Computing 3 (3) (1997), pp. 229–237.
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Shashikhin, V.N. Robust Control Using Interval Analysis. Reliable Computing 7, 219–230 (2001). https://doi.org/10.1023/A:1011446804678
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DOI: https://doi.org/10.1023/A:1011446804678