Robust stabilization of LTI negative imaginary systems using the nearest negative imaginary controller
Copyright policy )Robust stabilization of LTI negative imaginary systems using the nearest negative imaginary controller
Abstract This paper considers the problem of robust stabilization of linear time‐invariant systems with respect to unmodelled dynamics and structure uncertainties. To that end, a methodology to find the nearest negative imaginary system for a given non‐negative imaginary system is presented first. Then, this result is employed to construct a near optimal linear quadratic Gaussian controller achieving desired performance measures. The problem is formulated using port‐Hamiltonian method and the required conditions are defined in terms of linear matrix inequalities. The technique is presented using the fast gradient method to solve the problem systematically. The designed controller satisfies a negative imaginary property and guarantees a robust feedback loop. The effectiveness of the approach is demonstrated by a simulation on a numerical example.
- Qatar University Qatar
- Prince Sultan University Saudi Arabia
- Assiut University Egypt
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Iterative Learning Control in Engineering Practice, Artificial intelligence, Morphing Aircraft Technology, Iterative Learning Control, Robustness (evolution), Robust control, Aerospace Engineering, FOS: Mechanical engineering, Geometry, Control (management), Mathematical analysis, Biochemistry, Gene, Control Issues in Nanopositioning Systems, Engineering, Linear system, Control theory (sociology), FOS: Mathematics, Psychology, Control system, Biology, Control engineering systems. Automatic machinery (General), linear quadratic Gaussian control, Controller (irrigation), Mathematical optimization, linear systems, Quadratic equation, Linear matrix inequality, Computer science, Agronomy, The Imaginary, FOS: Psychology, Chemistry, LTI system theory, Control and Systems Engineering, TJ212-225, Electrical engineering, Physical Sciences, Psychotherapist, negative imaginary system, Nonlinear Systems, Mathematics
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