Analysis and synthesis of uncertain time-varying control systems

Dr Sanjay Lall (California Institute of Technology)

In this talk, we will discuss new developments in the theory of linear, time-varying (LTV) systems, focusing on the construction of a new multidimensional transform with properties similar to that of frequency. In particular, we will show that using this transformation, LTV problems are strongly connected to mu-theory.

Previous methods for robust analysis and synthesis of LTV systems have focussed on Riccati equations. In comparison, uncertain time-invariant problems have been formulated to take advantage of convex methods, and this has enabled analysis of integral-quadratic constraints (IQCs) and other uncertainty structures. These methods have taken advantage of the frequency domain for time-invariant systems, and the corresponding mu problem structure.

In the new framework, a convex solution for certain robustness problems is developed for LTV systems which parallels the solution in the time-invariant case. One of the advantages of the new framework is that there is a formal correspondence between LTI and LTV problems, which indicates potential for direct generalization of known LTI robust control results, including model reduction and recent robust synthesis techniques.

Applications include control analysis and synthesis of multi-rate sampled-data systems, and the computation of robustness margins for dynamical systems subject to perturbations along specified trajectories.

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