An Lmi Approach to Robust H∞ Control for Uncertain Continuous-Time Systems

Abstract

This paper investigates the problems of robust H ∞ control for uncertain continuous-time systems with time-varying, norm-bounded uncertainties in all system matrices. Necessary and sufficient conditions for the above problems are proposed. All conditions are represented in the form of linear matrix inequalities (LMIs). The robust H ∞ controller can be easily designed from the solutions of the LMI conditions. Unlike earlier works, the proposed method does not involve any parameter tuning. Thus the robust H ∞ optimization control problem, which has not been discussed in earlier reports, can be dealt with using this newly proposed method.

Majorant-Based Control Methodology for Mechatronic and Transportation Processes

“…Proof: If ẏ(t) is affected by a bounded measurement error n y (1) then w has an increase equal to 1) 2aHn y (1) , 3aHn y (1) , 4aHn y (1) , in cases S2, S6, S9 2) 6a 2 Hn y (1) , 12a 2 Hn y (1) , in cases S3, S7 3) 16a 3 Hn y (1) , in case S4, and γ c has an increase not greater than 1) max 2aHn y (1) , max 3aHn y (1) , max 4aHn y (1) , in cases S2, S6, S9 2) max 6a 2 Hn y (1) , max 12a 2 Hn y (1) , in cases S3, S7 3) max 16a 3 Hn y (1) , in case S4. On the other hand, note that e(t) is 1) inversely proportional to a 2 in case S2, a 3 in case S6, a 4 in case S9;…”

“…Theorem 6: If ẏ(t), ÿ(t), ... y (t) are affected by bounded measurement errors n y (1) , n y (2) , n y (3) , the increase of the tracking error norm e(t) is inversely proportional to a or a 2 or a 3 .…”

“…On the other hand, some popular adaptive control techniques (see e.g., [13], [24], [42]) and linear matrix inequality (LMI) approaches often turn out to be quite complex and arise criticisms from a practical point of view (see e.g., [2], [12], [28]). Recently, also fuzzy control methods deal with the above matters in specific cases (see e.g., [14], [18], [25], [30]).…”

Robust tracking design for uncertain MIMO systems using proportional–integral controller of order v

“…[1][2][3][4][5][6][7]), including recent ones [8][9][10][11][12][13][14][15][16][17][18][19][20]. However, the following practical limitations still remain in effect: (a) the considered classes of systems are often of particular structure; (b) the considered reference signals and disturbances almost always have standard waveforms (polynomial and/or sinusoidal ones); (c) the controllers are not robust enough and/or do not applicable to systems satisfying more than one specification; (d) the control inputs are excessive and/or unfeasible in some cases [1][2][3][4][5][6][7][8][9][10][11][21][22][23][24][25][26][27][28].…”

H? Control of Discrete-time Uncertain Periodic Systems with Delays

“…This has impulsed a large number of research results obtained on the analysis and synthesis for discrete and continuous-time uncertain system; see, e.g. [10,12,3,8,2,7,9]. Many researchers have extended the obtained results on the robust H ∞ control for delayed systems.…”