On the synthesis of variable structure observers for LPV systems

In this paper, an analysis and synthesis framework for a class of robust variable structure observers for linear parameter varying (LPV) systems is proposed. Instead of satisfying passivity-like conditions, the variable structure observer is created by ensuring a small gain condition is satisfied, formulated via loop transformations. The transformation of the problem into a small gain formulation allows a number of existing techniques from the literature to be conveniently exploited to synthesize the observer gains. The observer gains are computed by solving a set of linear matrix inequalities based on using an affine parameter-dependent Lyapunov function that helps reduce any design conservatism. The scheme is applied to an LPV model of the short period dynamics of a commercial aircraft to demonstrate its robustness.