Robust Pole Placement in LMI Regions - Pierre Apkarian
(1). whereÐУ andGЦ are real matrices such thatgУШ Xd У . The matrix- valued function. h i ... the LMI regionХР, if and only if there exists a symmetric. matrixI such that. Ц ..... withstand neglected dynamics and1fl exible modes. ⢠Maximum de fl ...
regions, a class of convex regions of the complex plane that embraces most practically .... R and C denote the sets of real and complex numbers, respectively.
where Q is a L x L symmetric matrix, qT Ñ (RL) and p Ñ R. Ñ denotes a hyper-rectangle in the positive ...... 0 .04321 9 - 0 .010111 0 .1441 9 5 6 8. Pi = 10 -5 '.
bilinear constraints can be formulated as the minimization of a concave functional ... constraints (see e.g. [20, 9]) which are very hard nonconvex optimization.
quential Quadratic Programming (SQP) known in nonlinear optimization. ...... d o conclude the proof, let us multiply equation ( 3 ) above by x X ax, and divide by.
resentation) uncertain systems depending on a time-varying parameter uncertainty. .... As concave programming is the best studied class of problems in global ...... problem by the introduction of one extra variable, whereas the simplicical ...
as quadratic functionals in and by a Schur's com- ... Again, rewriting the left-hand side of (36) as a quadratic functional in .... Equation (9). (10): Rewrite (10) as.
Reliable and efficient techniques are now available to synthesize gain-scheduled controllers. Such tech- .... to accuracy with the above technique. The trape z ...
classical linear fractional transformation (LFT) representations. ... in scaling variables, while those of [12] are in the form of exact LMIs. ... discrete-time systems.
Sep 13, 1994 - This paper is concerned with the robust control problem of plants ... It alternates analysis phases and synthesis phases both ..... N o w the characteriz ation in ( 1 8 ) - (жР0) is a con v ex feasibility program in the v ariables 7
approaches to control law design.ба number of different nonlinear tech- ..... conservative for three reasons ¢ that ¢ is treated as a complex number, that.
robust synthesis problem shown schematically in Fig. 1. In sec- tion III we discuss ...... In Table II the results of inner relaxation from algorithm. 1, hybrid approach ...
Feb 20, 2012 - Results in terms of achieved HÑ objectives and running times are displayed .... AC13. 28/7/110. 120.94. 29.56. 157.38. 156.33. AC14. 40/0/12.
A comparative graphical view of the achieved objective values as well as execution times for both techniques is given in figure 1. The top plots in figure. 1 shows ...
AbstractâThe Power Oscillation Damping (POD) controllers implemented in the two ..... is represented by the standard form description (u â Rm2 and y â Rp2 ) ...
trix inequality (LMI) optimization formulations for un- certain NFT discrete systems with performance crite- ria based on generalized H2 and Hâ norm constraints.
number of decision variables, the proposed techniques o ff er a valuable alternative to S ... F and C denotes the sets of real and complex numbers, respectively.
where Ccl = [L âLF ] and P is the solution of the Lyapunov equation ... dependent Lyapunov functions are far less conservative than customary fixed quadratic.
as Linear Ð atrix I nequalities ( L ÐI) optimiвб ation problems [7, 10], which are then ... to our definitions, the pairw7ym Y lm @ is the gain-scheduling channel. ...... [5] J .- Ð . Ð iannic and P. Ap arian, Missile Autopilot Design via a mod
Convex quadratic constraints can be rewritten. (Ax + b). â² .... convert family of constrained quadratic inequalities ..... Easily computed by solving linear equation.
Paul Sabatier University, Maths. ... These mathematical concepts indicate at least the ... Clarke subdifferential of several nonconvex composite functions f(x) ... at G [8]. More generally, assume that the columns of Qu form an orthonormal basis of t
Significant progress in control design has been achieved by the use of ... idea of the diligent use of nonsmooth criteria of the form f(K) = maxÏâ[0,â] λ1 (F(K, Ï)) ...
