On robust and \({\mathcal H}_ \infty\) controls for a class of linear and bilinear systems with nonlinear uncertainty
The paper is a contribution to a Lyapunov based approach to robust control system design [see e.g. \textit{G. Leitmann}, J. Dyn. Syst. Meat. Control 101, 212-216 (1979; Zbl 0416.93077), \textit{B. R. Barmish}, \textit{M. Corless} and \textit{G. Leitmann}, SIAM J. Contr. Optim. 21, 246-255 (1983; Zbl 0503.93049)]. The authors consider nominally linear and bilinear systems with cone bounded uncertainties and propose a modification of a quadratically stabilizing feedback law introduced in [\textit{B. R. Barmish}, J. Optim. Theory Appl. 46, 399-408 (1985; Zbl 0564.93051)]. The control law ensures uniform exponential stability of the resulting closed loop system and incorporates to the problem of \(H^\infty\) robustness of the system. Conditions imposed on the matrices used to design the control law could be in special cases fulfilled by solutions of linear matrix inequalities leading to a simplification of the synthesis problem. In the case of bilinear uncertain systems the authors follow the line of reasoning propoposed in [\textit{P. O. Gutman}, IEEE Trans. Autom. Control AC-26, 917-922 (1981; Zbl 0552.93046)] strengthening conditions imposed on the matrix used in the designed feedback control law. The paper suffers from some uncorrected mistakes.
scientific article; zbMATH DE number 1062907