Date of Award


Document Type


Degree Name

Master of Science in Engineering (MSE)


Electrical and Computer Engineering

Committee Chair

Yuri Shtessel

Committee Member

Craig H. Newborn

Committee Member

Timothy Boykin


Nonlinear control theory, Robust control


In this thesis, new definitions of Practical Phase and Gain stability margins (PPM/PGM) for a class of nonlinear systems (a single-input-single output linear time invariant (SISO LTI) plant with a nonlinear control), specifically, in systems with common nonlinearities like saturation and relay, are proposed. The practical Gain and Phase stability margins are presented as the maximum increase in the gain and the maximum phase shift that can added to the frequency characteristic of the linear plant such that there are no limit cycles predicted or the sufficient stability condition is satisfied. The stability margins are computed using the Describing-Function-Harmonic-Balance (DF-HB) technique and the Circle Criteria. Both methods are compared and analysed. Tutorial examples are presented to demonstrate the efficacy of the proposed algorithms for systems with saturation and relay with a dead-band. Also, a case study of the flight control systems with saturation demonstrates the effectiveness of the proposed approach.



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