Artículos de revistas
Extended H2 And H∞ Norm Characterizations And Controller Parametrizations For Discrete-time Systems
Registro en:
International Journal Of Control. , v. 75, n. 9, p. 666 - 679, 2002.
207179
10.1080/00207170210140212
2-s2.0-0037096509
Autor
De Oliveira M.C.
Geromel J.C.
Bernussou J.
Institución
Resumen
This paper presents new synthesis procedures for discrete-time linear systems. It is based on a recently developed stability condition which contains as particular cases both the celebrated Lyapunov theorem for precisely known systems and the quadratic stability condition for systems with uncertain parameters. These new synthesis conditions have some nice properties: (a) they can be expressed in terms of LMI (linear matrix inequalities) and (b) the optimization variables associated with the controller parameters are independent of the symmetric matrix that defines a quadratic Lyapunov function used to test stability. This second feature is important for several reasons. First, structural constraints, as those appearing in the decentralized and static output-feedback control design, can be addressed less conservatively. Second, parameter dependent Lyapunov function can be considered with a very positive impact on the design of robust H2 and H∞ control problems. Third, the design of controller with mixed objectives (also gain-scheduled controllers) can be addressed without employing a unique Lyapunov matrix to test all objectives (scheduled operation points). The theory is illustrated by several numerical examples. 75 9 666 679 Barmish, B.R., Necessary and sufficient conditions for quadratic stabilizability of an uncertain system (1985) Journal of Optimization Theory and Application, 46, pp. 399-408 Bernussou, J., Geromel, J.C., Peres, P.L.D., A linear programming oriented procedure for quadratic stabilization of uncertain systems (1989) Systems and Control Letters, 13, pp. 65-72 Colaneri, P., Geromel, J.C., Locatelli, A., (1997) Control Theory and Design: An RH2-RH∞ Viewpoint, , San Diego, CA: Academic Press De Oliveira, M.C., Bernussou, J., Geromel, J.C., A new discrete-time robust stability condition (1999) Systems and Control Letters, 37, pp. 261-265 De Oliveira, M.C., Geromel, J.C., Bernussou, J., An LMI optimization approach to multiobjective controller design for discrete-time systems (1999) Proceedings of the 38th IEEE Conference on Decision and Control, pp. 3611-3616. , Phoenix, AZ, USA De Oliveira, M.C., Geromel, J.C., Bernussou, J., Design of decentralized dynamic output feedback controllers via a separation procedure (2000) International Journal of Control, 73, pp. 371-381 Feron, E., Apkarian, P., Gahinet, P., Analysis and synthesis of robust control systems via parameter-dependent Lyapunov functions (1996) IEEE Transactions on Automatic Control, 41, pp. 1041-1046 Gahinet, P., Explicit controller formulas for LMI-based H∞ synthesis (1996) Automatica, 32, pp. 1007-1014 Geromel, J.C., Bernussou, J., De Oliveira, M.C., H2 norm optimization with constrained dynamic output feedback controllers: Decentralized and reliable control (1999) IEEE Transactions on Automatic Control, 44, pp. 1449-1454 Geromel, J.C., Bernussou, J., Peres, P.L.D., Decentralized control through parameter space optimization (1994) Automatica, 30, pp. 1565-1578 Geromel, J.C., De Oliveira, M.C., Bernussou, J., Robust filtering of discrete-time linear systems with parameter dependent Lyapunov functions (1999) Proceedings of the 38th IEEE Conference on Decisions and Control, pp. 570-575. , Phoenix, AZ, USA Geromel, J.C., Peres, P.L.D., Bernussou, J., On a convex parameter space method for linear control design of uncertain systems (1991) SIAM Journal on Control and Optimization, 29, pp. 381-402 Geromel, J.C., Peres, P.L.D., De Souza, S.R., A convex approach to the mixed H2/H∞ control problem for discrete time uncertain systems (1995) SIAM Journal on Control and Optimization, 33, pp. 1816-1833 Geromel, J.C., Peres, P.L.D., De Souza, S.R., Convex analysis of output feedback control problems: Robust stability and performance (1996) IEEE Transactions on Automatic Control, 41, pp. 997-1003 Khargonekar, P.P., Rotea, M.A., Mixed H2/H∞ control: A convex optimization approach (1991) IEEE Transactions on Automatic Control, 39, pp. 824-837 Masubuchi, I., Ohara, A., Suda, N., LMI-based controller synthesis: A unified formulation and solution (1998) International Journal of Robust and Nonlinear Control, 8, pp. 669-686 Scherer, C.W., Gahinet, P., Chilali, M., Multiobjective output-feedback control via LMI optimization (1997) IEEE Transactions on Automatic Control, 42, pp. 896-911 Siljak, D.D., (1978) Large Scale Dynamic Systems: Stability and Structure, , NJ: North Holland Veillette, R.J., Medanic, S.V., Perkins, W.R., Design of reliable control systems (1992) IEEE Transactions on Automatic Control, 37, pp. 280-304