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Robust state-derivative feedback LMI-based designs for multivariable linear systems. (English) Zbl 1133.93022
Summary: In some practical problems, for instance in the control systems for the suppression of vibration in mechanical systems, the state-derivative signals are easier to obtain than the state signals. New necessary and sufficient linear matrix inequalities (LMI) conditions for the design of state-derivative feedback for multi-input (MI) linear systems are proposed. For multi-input/multi-output (MIMO) linear time-invariant or time-varying plants, with or without uncertainties in their parameters, the proposed methods can include in the LMI-based control designs the specifications of the decay rate, bounds on the output peak, and bounds on the state-derivative feedback matrix $$K$$. These design procedures allow new specifications and also, they consider a broader class of plants than the related results available in the literature. The LMIs, when feasible, can be efficiently solved using convex programming techniques. Practical applications illustrate the efficiency of the proposed methods.

##### MSC:
 93B52 Feedback control 93C35 Multivariable systems, multidimensional control systems 90C25 Convex programming 93C05 Linear systems in control theory
LMI toolbox
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##### References:
 [1] DOI: 10.1049/ip-cta:20040660 [2] Abdelaziz THS, Kybernetika 41 pp 637– (2005) [3] Assunção E, Proceedings of the 38th IEEE Conference on Decision and Control pp 1857– (1999) [4] DOI: 10.1080/00207720601053568 · Zbl 1148.93011 [5] DOI: 10.1109/TPEL.2004.830042 [6] Boyd S, Linear Matrix Inequalities in Systems Control Theory (1994) [7] de Oliveira MC, LMISol, User’s Guide (1997) [8] DOI: 10.1111/j.1934-6093.2003.tb00125.x [9] Duan GR, Proceedings of the 1999 American Control Conference 1999 pp 1304– [10] DOI: 10.1111/j.1467-8667.2005.00396.x [11] DOI: 10.1137/1.9780898719833 · Zbl 0932.00034 [12] DOI: 10.1016/S0024-3795(01)00563-8 · Zbl 1006.93021 [13] Gahinet P, LMI Control Toolbox – For use with Matlab (1995) [14] DOI: 10.1049/ip-cta:20045041 [15] DOI: 10.1016/0167-6911(94)90025-6 · Zbl 0801.93032 [16] DOI: 10.1016/j.automatica.2004.01.028 · Zbl 1051.93042 [17] DOI: 10.1061/(ASCE)0893-1321(2002)15:1(1) [18] DOI: 10.1006/jsvi.2001.3842 · Zbl 1237.93127 [19] Nesterov Y, Interior-Point Polynomial Algorithms in Convex Programming (1994) · Zbl 0824.90112 [20] Palhares RM, Int. J. Comp. Res. 12 pp 115– (2003) [21] Reithmeier E, Arc. Appl. Mech. 72 pp 856– (2003) [22] Slotine JJE, Appl. Non-linear Cont. (1991) [23] DOI: 10.1109/TFUZZ.2003.817840 [24] DOI: 10.3166/ejc.11.167-170 [25] DOI: 10.1109/VSS.2006.1644539
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