Robust performance analysis for systems with norm-bounded time-varying structured uncertainty

This paper analyses robust performance measures for linear time-invariant systems with norm-bounded time-varying structured uncertainty. We consider two robust performance measures. One is the worst case peak value of the error signal in response to the disturbance with a known energy. The other is the worst case energy of the error signal in response to impulsive disturbance. In both cases, the "worst case" is taken over all admissible uncertainties and disturbances. The notion of robust stability is Q-stability, or the scaled H/sub /spl infin//, norm bound. Our main results provide an upper bound for each of the robust performance measures in terms of a positive definite matrix which satisfies a linear matrix inequality (LMI) together with a scaling matrix. Hence, the best bound in this LMI formulation can be computed by convex programming.

[1]  John C. Doyle.  Analysis of Feedback Systems with Structured Uncertainty , 1982 .

[2]  J. Doyle.  Synthesis of robust controllers and filters , 1983, The 22nd IEEE Conference on Decision and Control.

[3]  Michael Safonov,et al.  L∞-optimal sensitivity vs. stability margin , 1983, The 22nd IEEE Conference on Decision and Control.

[4]  J. Doyle,et al.  Minimizing Conservativeness of Robustness Singular Values , 1984 .

[5]  D. Wilson.  Convolution and Hankel operator norms for linear systems , 1989 .

[6]  Reduction of conservatism in mixed H/sub 2//H/sub infinity / control design , 1989, Proceedings of the 28th IEEE Conference on Decision and Control,.

[7]  D. Bernstein,et al.  Robust stability and performance analysis for state-space systems via quadratic Lyapunov bounds , 1990 .

[8]  P. Khargonekar,et al.  Robust stabilization of uncertain linear systems: quadratic stabilizability and H/sup infinity / control theory , 1990 .

[9]  J. Doyle,et al.  Review of LFTs, LMIs, and mu , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

[10]  A. Stoorvogel.  The robust H2 control problem: a worst-case design , 1993, IEEE Trans. Autom. Control..

[11]  J. P. Chretien,et al.  μ synthesis by D - K iterations with constant scaling , 1993, 1993 American Control Conference.

[12]  Andrew Packard,et al.  The complex structured singular value , 1993, Autom..

[13]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .