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

Abstract

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 H 2 or the H 1 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.

Stochastic H<inf>&#x221E;</inf> Static output-feedback control of state-multiplicative discrete-time systems with delay

“…The full order dynamic output-feedback problem for stochastic retarded systems was solved in [8], for nominal systems and normbounded uncertain ones. Recently [9], An extended solution which includes a reduced-order controllers, including the full order case, was applied to retarded continuous-time statemultiplicative stochastic systems where the inclusion of a low pass filter as in [7] was avoided. In the stochastic discretetime delayed counterpart setting, which has been addressed to a lesser extent comparing to the continuous-time case, the mean square exponential stability and the control and filtering problems of these systems were treated by several groups [10]- [13].…”

“…The main advantage of the static output-feedback is the simplicity of its implementation and the ability it provides for designing controllers of prescribed structure such as PI and PID. In the stochastic setting, the problem of zero-order control was addressed by [7] for continuous-time delay-free systems where, by adding a simple component of large bandwidth to the measured output, achieves tighter bounds on the H 2 and the H ∞ performance criteria, when numerically compared to other design techniques [7]. The full order dynamic output-feedback problem for stochastic retarded systems was solved in [8], for nominal systems and normbounded uncertain ones.…”