Linear parameter varying systems: A geometric theory and applications

Regularly and Singularly Perturbed Systems Design Goal and Reference Model Methods of Control System Design Under Uncertainty Design of SISO Continuous-Time Control Systems Advanced Design of SISO Continuous-Time Control Systems Influence of Unmodeled Dynamics Realizability of Desired Output Behavior Design of MIMO Continuous-Time Control Systems Stabilization of Internal Dynamics Digital Controller Design Based on Pseudo-Continuous Approach Design of Discrete-Time Control Systems Design of Sampled-Data Control Systems Control of Distributed Parameter Systems.

Design of Nonlinear Control Systems with the Highest Derivative in Feedback

Linear Parameter Varying (LPV) systems appear in a form of LTI state space representations where the elements of the A(rho), B(rho), C(rho) matrices depend on an unknown but at any time instant measurable vector parameter rho isin V. This paper describes a geometric view of LPV systems. Geometric concepts and tools of invariant subspaces and algorithms for LPV systems afflne in the parameters will be presented and proposed. Application of these results will be shown and referenced in solving various analysis (controllability/observability) problems, controller design and fault detection problems associated to LPV systems.

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Geometric Theory and Control of Linear Parameter Varying Systems

A simple controller based on a second order active filter is applied to extend the synchronization region of a forced weakly nonlinear self-sustained oscillator. The controller stabilizes unstable periodic orbits that exist in the uncontrolled system outside the synchronization region. The control algorithm is non-invasive in the sense that it uses only small control perturbations. We present analytical and numerical results as well as an experimental demonstration.

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Control of synchronization via a second order filter controller

In this work, the adaptive control scheme for a class of input-output linearizable nonlinear systems subjected to system uncertainties is presented. An adaptation law is proposed to estimate unknown system parameters such that the effect of the system parameter uncertainties can be reduced and a switching state feedback gain is set in the adaptive control input to treat with unmodelled dynamical uncertainty problems. Then a robust adaptive control scheme in the presence of the above system uncertainties can be ensured. It is further indicated that the proposed adaptive control scheme will be robust asymptotically stable under some modifications. Some computer simulation results are proposed to show the performance of the proposed adaptive control scheme.

S. D. Katebi

Papers

Nonlinear dynamical control systems, H. Nimeijer and A. J. Van der Schaft, Springer Verlag, Berlin, 1990, xiii + 467 pp., ISBN 3–540-97234-x, DM 98.00