Robust stability and performance of systems with structured and bounded uncertainties: an extension of the guaranteed cost control approach

Abstract

Robust stability and performance of systems with structured and bounded uncertainties: an extension of the guaranteed cost control approach O. I. KOSMIDOUt A method is presented for designing a full state feedback linear control law that will ensure the robust stability and performance of a given linear uncertain system. The systems under consideration are described by state equations that depend on uncertain parameters. These uncertain parameters may be time varying. Their values are constrained to lie within known compact bounding sets. The method is based on the guaranteed cost control concept of Chang and Peng (1972). The controller gains result from the solution of a Riccati equation in which the weighting matrices depend on the uncertainty bounds. Sufficient conditions for the existence of a solution arise from the standard LQG control theory.(I)

Comments on ‘Robust stability and performance of system with structured and bounded uncertainties: an extension of the guaranteed cost control approach’

“…Unfortunately, as illustrated by the following example, the main results of Kosmidou (1990) are incorrect.…”

“…If we choose the design parameter al = 51 then, from (12), (14), (15), (30), (31) and (39) of Kosmidou (1990) …”

“…This example (Kosmidou 1990) is an application of robust design methods to a remotely piloted vehicle (RPV) flight control system, which has also been discussed by Vinkler and Wood (1978) and Kosmidou and Bertrand (1987).…”

“…In a recent paper (Kosmidou 1990), by using a similar upper bound function of the uncertainties to that used by Liou and Yang (1987), Kosmidou extends the guaranteed cost control (GCe) of Chang and Peng (1972) to the case where both the system dynamics matrix and the input matrix contain uncertainties. Unfortunately, as illustrated by the following example, the main results of Kosmidou (1990) are incorrect.…”

On the Riccati Equations Arising in Robust Control Approaches

“…In the case of the approaches in Theo- then ( ) U P obtains a specific form for which the resulting MRE reduces to the standard Riccati equation form [13]. Besides, in the particular case where the system uncertainties affect only the state matrix i.e.…”