In this paper we show how some difficult linear algebra problems can be “approximately” solved using statistical learning methods.We illustrate our results by considering the state and output feedback, finite-time robust stabilization problems for linear systems subject to timevarying norm-bounded uncertainties and to unknown disturbances. In the state feedback case, the paper provides a sufficient condition for finite-time stabilization in the presence of timevarying disturbances; such condition requires the solution of a linear matrix inequality (LMI) feasibility problem, which is by now a standard application of linear algebraic methods. In the output feedback case, however, we end up with a bilinear matrix inequality (BMI) problem which we tackle by resorting to a statistical approach. © 2002 Elsevier Science Inc. All rights reserved.
Statistical learning methods in linear algebra and control problems: the example of finite-time control of uncertain linear systems / Abdallah, C. T.; Amato, F.; Ariola, M.; Dorato, P.; Koltchinskii, V.. - In: LINEAR ALGEBRA AND ITS APPLICATIONS. - ISSN 0024-3795. - 351-2:(2002), pp. 11-26.
Statistical learning methods in linear algebra and control problems: the example of finite-time control of uncertain linear systems
F. Amato;
2002
Abstract
In this paper we show how some difficult linear algebra problems can be “approximately” solved using statistical learning methods.We illustrate our results by considering the state and output feedback, finite-time robust stabilization problems for linear systems subject to timevarying norm-bounded uncertainties and to unknown disturbances. In the state feedback case, the paper provides a sufficient condition for finite-time stabilization in the presence of timevarying disturbances; such condition requires the solution of a linear matrix inequality (LMI) feasibility problem, which is by now a standard application of linear algebraic methods. In the output feedback case, however, we end up with a bilinear matrix inequality (BMI) problem which we tackle by resorting to a statistical approach. © 2002 Elsevier Science Inc. All rights reserved.File | Dimensione | Formato | |
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