Anisotropy-based analysis for finite horizon time-varying systems with non-centered disturbances
We consider the problem of anisotropy-based analysis of the robust quality linear discrete time-varying systems with finite horizon under random external disturbance. Uncertainty in the probability distributions of disturbance vectors is found with the information-theoretic notion of anisotropy and additional conditions on the first two moments. The quality of operation of the object is defined by the value of the anisotropic norm of the input-output matrix corresponding to the system. We show that computing the anisotropic norm of a time-varying system in the state space with non-centered disturbance is related to solving a system of difference matrix equations and equations of a special form. We show a sample computation of the anisotropic norm for a time-varying system with finite horizon.
Keywordsanisotropy-based control theory non-centered random signals linear discrete time-varying system
Unable to display preview. Download preview PDF.
- 8.Semyonov, A.V., Vladimirov, I.G., and Kurdjukov, A.P, Stochastic Approach to H∞-Optimization, Proc. 33 IEEE Conf. Dec. Control., 1994, vol. 3, pp. 2249–2250.Google Scholar
- 10.Vladimirov, I.G., Kurdjukov, A.P., and Semyonov, A.V, On Computing the Anisotropic Norm of Linear Discrete-Time-Invariant Systems, Proc. 13th IFAC World Congress, San-Francisco, USA, 1996, pp. 179–184.Google Scholar
- 11.Vladimirov, I.G., Kurdjukov, A.P., and Semyonov, A.V., State-Space Solution to Anisotropy-Based Stochastic H∞-Optimization Problem, Proc. 13 IFAC World Congress, San Francisco, 1996, vol. H, pp. 427–432.Google Scholar
- 14.Maximov, E.A., Kurdyukov, A.P., and Vladimirov, I.G, Anisotropy-Based Bounded Real Lemma for Linear Discrete Time Varying Systems, Proc. 18 IFAC World Congress, Milano, Italy, 2011, pp. 4701–4706.Google Scholar
- 15.Kurdyukov, A., Kustov, A., Tchaikovsky, M., and Karny, M, The Concept of Mean Anisotropy of Signals with Nonzero Mean, Proc. Int. Conf. Process Control, Strbske Pleso, Slovakia, 2013, pp. 37–41.Google Scholar
- 18.Lofberg, J., YALMIP: A Toolbox for Modeling and Optimization in MATLAB, Proc. CACSD Conf., Taipei, Taiwan, 2004. http://users.isy.liu.se/johanl/yalmip/Google Scholar