Parameter-Dependent Lyapunov Functions for Real ... - Pierre Apkarian
1 . each parameter Q is real and ranges bet ( eenÐI no ( n extremal values Q and S Q : ... but the coefficients of a convex decomposition of over the set {3 Ц254 &6 &7 & 4 ...... robustness measures such as the μ structured singular value or the ...
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 '.
Email: {s3shung, tuan, n-tatsuo}@toyota-ti.ac.jp. ââ ... proach is due to the non-trivial step of identifying convex or concave ... 2 addresses the adaptive backstepping problem for the system (1) in .... tive controller for system (1) with a new
Since an optimization algorithm for (4) will converge to a solution on the boundary of ...... Series in Operations Research, 2000. ... with design applications.
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.
incorporation of multiple specifications into the design problem such as Hзжй .... vt ) T nЧu X uw i h g fUd ll d wYT ng T nfinÐTWipg -eqT m#g n§RhTd nÐP l ...... motor and a concentrated mass at the tip of the second beam which is the payload
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
classical linear fractional transformation (LFT) representations. ... in scaling variables, while those of [12] are in the form of exact LMIs. ... discrete-time systems.
The method is conveniently implemented with available. SDP interior-point solvers. ... In this paper, we follow a quite diff erent line of attack initiated in [1] .
N o w consider a S c h ur decomposition of t h e matrix ¡ and a partition of t ... `8 = X * 8 is non singular ( in proposition 2 .3 , a necessar y condition for 8 to be full column ...... S imilar computations y ield t h e follo w ing numerical valu
The synthesis of flight control laws for modern aeronautics and space applications re- ... First of all, time-domain specifications should be addressed indirectly via nontrivial tuning .... notes the peak value of the transfer function maximum singul
gradients, superlinear and quadratic convergence, bilinear matrix inequality ..... way to describe it is to say that the Jacobian of the set of equations h1 (F(x)) =.
Implicit Model Following Formulation. Paulo C. Pellandaâ ... Following (IMF) is considered in the context of Linear ... desired dynamic behavior and that of the closed-loop system. ..... practically valid alternative to pole-based methods for.
When αâ < 0 every solution x(t) of (3) decays at least as fast as eαât, in which case .... Suppose algorithm 1 is operated with a con- sistent pruning test 乡 and ...
approaches to control law design.ба number of different nonlinear tech- ..... conservative for three reasons ¢ that ¢ is treated as a complex number, that.
to single-input single-output systems, even though some multivariable ... closed-loop stability has to be modelled as a mathematical programming .... introduction to the salient features we refer the reader to [3,17], and to [16] for variations of th
sis, either as a stand-alone task, or to initialize algorithms for Hâ synthesis or related problems. .... this research is a package HIFOO, which will be included in our tests, see section 6. ..... II of the descent algorithm in the following appli
The general nature of BMI problems, which include for instance quadratic con- ...... The corresponding quadratic equation has two real solutions, and the positive.
PROBLEMS : APPLICATIONS TO CONTROL DESIGN .... ing B(x) â¼ 0, where the algorithm makes no further ...... ematics of Operations Research, 21:576â588.
