Resilient nonlinear observer design via linear matrix inequalities

Chung Seop Jeong, Marquette University


Much of the recent work on robust control or observer design has focused on preservation of stability of the controlled system or the convergence of the observer in the presence of parameter perturbations in the plant equations. The present dissertation addresses an important problem of resilience or non-fragility for linear and nonlinear state observes, which is the maintenance of convergence and/or performance when the observer gain is erroneously implemented due possibly to computational errors i.e. round off errors in computing the observer gain or changes in the observer parameters during operation. Designing resilient linear observers, those will not be destabilized by small perturbations in the observer gains will be discussed, first. Observers for both discrete time and continuous time systems with deterministic or stochastic gain perturbations will be considered for this matter. For designing nonlinear observers, the problem of deterministic gain perturbations in Thau's observer for both the discrete-time and continuous-time will be considered. This will be followed by the discussion of designing nonlinear observers with general criteria for both discrete-time and continuous-time systems. Designing of resilient discrete-time observers with general criteria and stochastically resilient design of H∞ observers for discrete-time nonlinear systems will also be discussed. Linear Matrix Inequalities techniques will be applied as a "tool" to solve the design problem. Several illustrative simulation examples will be included to show the effectiveness of the proposed methodology.

Recommended Citation

Jeong, Chung Seop, "Resilient nonlinear observer design via linear matrix inequalities" (2007). Dissertations (1962 - 2010) Access via Proquest Digital Dissertations. AAI3263810.