Static output-feedback of state-multiplicative systems with application to altitude control

A linear parameter dependent approach for designing a constant output-feedback controller for a linear time-invariant system with stochastic multiplicative Wiener-type noise, that achieves a minimum bound on either the stochastic H₂ or the H∞ performance level is introduced. A solution is achieved also for the case where in addition to the stochastic parameters, the system matrices reside in a given polytope. In this case, a parameter dependent Lyapunov function is introduced which enables the derivation of the required constant gain via a solution of a set of linear matrix inequalities that corresponds to the vertices of the uncertainty polytope. The stochastic uncertainties appear in both the dynamic and the measurement matrices of the system. The problems are solved using the expected value of the standard performance index over the stochastic parameters. The theory developed is applied to an altitude control example.