Analysis and control of uncertain/nonlinear systems in the presence of bounded disturbance inputs

Trent Alan Pancake, Purdue University

Abstract

Real world dynamic systems are frequently subjected to unknown disturbance inputs or perturbations. These inputs are difficult to model but must be taken into account in system analysis and control design, otherwise the integrity of the system could be compromised. When analyzing or controlling a system subjected to these types of disturbances, one is quite often concerned with the peak magnitude of some performance output. Clearly the peak magnitude of important variables is of concern in many engineering systems. This thesis begins by introducing the concept of L∞ stability with a level of performance γ. For zero initial state, γ is an upper bound on the L∞ gain of the system, that is, the gain of the system when viewed as an operator acting on L∞ inputs and producing L ∞ outputs. Using a Lyapunov based approach, a result which yields a sufficient condition for our notion of L∞ stability is introduced. This condition is applied to a variety of classes uncertain/nonlinear systems. These classes are characterized as polytopic uncertain/nonlinear systems, a general class of uncertain/nonlinear systems and general polytopic uncertain/nonlinear systems. For each of these classes this thesis states a bunch of linear matrix inequalities which, if satisfied, guarantee L∞ stability with a level of performance. This thesis also considers systems in which one cannot guarantee L∞ stability for the entire state-space. To this end, the notion of local L∞ stable with level of performance γ is introduced. These analysis results are then used to develop state-feedback controllers. The results in this thesis can be used to design disturbance attenuation controllers for the aforementioned classes of systems. Numerous examples are used to illustrate the results of the thesis.

Degree

Ph.D.

Advisors

Corless, Purdue University.

Subject Area

Aerospace engineering

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