SWITCHED STATE JUMP OBSERVERS FOR A CLASS OF NONLINEAR SWITCHED SYSTEMS

This paper addresses the problem of switched state ‘jump’ observer synthesis for a class of nonlinear switched systems for which the active mode is assumed to be unknown. The use of multiple quadratic Lyapunov functions and of the differential mean value theorem allows to transform the nonlinear error dynamics into a Linear Parameter Varying (LPV) system. Then we develop sufficient conditions for the observer synthesis that guarantee an upper bound on the estimation error. For a fixed value of a scalar parameter, the synthesis problem is brought to one of solving linear matrix inequalities (LMIs) that are easily tractable. A numerical example that demonstrates the applicability of our approach is also presented.