Robust and Resilient Control Design and Performance Analysis for Uncertain Systems with Finite Energy Disturbances

This dissertation addresses the problem of robust and resilient control design with additional performance analysis for uncertain systems with finite energy disturbances. The control design is robust and resilient in the sense of maintaining certain performance criteria in the presence of perturbations in both system parameters and feedback gains. The performance analysis evaluates resilience properties of state feedback and dynamic (state estimate) feedback controllers. A resilient and robust state feedback controller is designed using linear matrix inequality (LMI) techniques for the characterization of solutions to the analysis and design problems posed in this work. Uncertainties are allowed in the linear and nonlinear parts of the system model and also in the feedback gain so that the designed controller is robust in addition to being resilient. The design of controllers for various performance criteria including asymptotic stability, H2, Hinf, input strict passivity, output strict passivity and very strict passivity are presented. In addition to the design problem, an approach is presented for performance analysis of the resilience property of perturbed controller and observer gains. The resilience property is defined in terms of both multiplicative and additive perturbations on the gains so that the closed loop eigenvalues do not leave a specified region in the complex plane, such as a vertical strip, disk, sector region, etc. The method presented allows maximum gain perturbation bounds to be obtained based on the designer’s choices of controller eigenvalue region. The LMI technique is used also for the analysis process. Both design and analysis problems are treated using Lyapunov functions. All work is conducted for both continuous- and discrete-time cases. Several illustrative simulation examples are included to show the effectiveness of the proposed design and analysis approaches

Full- and reduced-order observer design for rectangular descriptor systems with unknown inputs

In this paper, methods are proposed to design Luenberger type full-and reduced-order observers for rectangular descriptor systems with unknown inputs. These methods are based on the effect of pre- and post-multiplicative operation of a linear transformation, derived here by means of simple matrix theory. Sufficient conditions for the existence of observers are given and proved. Numerical examples are given to illustrate the effectiveness of the proposed method