Estimation and control of non-linear and hybrid systems with applications to air-to-air guidance

Issued as Progress report, and Final report, Project no. E-21-67

Robust control of switched linear systems

Abstract-We consider robust control of switched linear systems under arbitrary time-dependent switching signals. First, we introduce a common quadratic Lyapunov function for the class of switched linear systems with Hurwitz constituent matrices in R n×n sharing n − 1 linearly independent common left eigenvectors. The common quadratic Lyapunov function is then used for robust stability analysis of the convexified differential inclusion associated with the underlying switched linear system. Finally, using the common left eigenstructure assignment approach for multi-input systems, robust design by means of state-feedback control is proposed

Feedback rectifiable pairs and stabilization of switched linear systems

We address the feedback design problem for switched linear systems. In particular we aim to design a switched state-feedback such that the resulting closed-loop switched system is in upper triangular form. To this effect we formulate and analyse the feedback rectification problem for pairs of matrices. We present necessary and sufficient conditions for the feedback rectifiability of pairs for two subsystems and give a constructive procedure to design stabilizing state-feedback for a class of switched systems. Several examples illustrate the characteristics of the problem considered and the application of the proposed constructive procedure

Observer designs for experimental non-smooth and discontinuous systems

This brief presents the design and implementation of observer design strategies for experimental non-smooth continuous and discontinuous systems. First, a piece-wise linear observer is implemented for an experimental setup consisting of a harmonically excited flexible steel beam with a one-sided support which can be considered as a benchmark for a class of flexible mechanical systems with one-sided restoring characteristics. Second, an observer is developed for an experimental setup that describes a dynamic rotor system which is a benchmark for motion systems with friction and flexibility. In both cases, the implemented observers guarantee global asymptotic stability of the estimation error dynamic in theory. Simulation and experimental results are presented to demonstrate the performance of the observers in practice. These results support the use of (switched) observers to achieve state reconstruction for such non-smooth and discontinuous mechanical systems