By Maksimov V. I.

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**Extra resources for A Boundary Control Problem for a Nonlinear Parabolic Equation**

**Example text**

3 the solution of the LDDPS is given using A s . 4 it is shown that stabilizability distri- butions also play a role in the solution of the Strong Local Input-0utput Decoupling Problem with Stability. 1) , y h(x), h(O) - 0 ~ y e 40 In this section we introduce the concept of stabilizability distribution which plays a key role in the solution of the LDDPS for nonlinear systems. We show that, under certain assumptions, the largest stabilizability distribution in the kernel of the output mapping (denoted by A~) exists.

18 very well be input-output decoupled as follows ([NvdS4]) [] deeoupled without being from the following example. 15) I = LgL~h(x) r(x) = ~ ~ if 1 3x~, ' so r(x) - Obviously, h(x) - 2 if the x1 x a ~ 0. conditions around x 0 - 0 are not fulfilled. ~ 2 12x2uu + Jxau 6u a + [0] ~ x a = 0. decouplability yC4> so the output g(x) ' Moreover, for strong However, (2) is indeed influenced by the input, whatever initial condition x o is chosen. 19 chapters in ker is played by the dh. ,m} the A N G u sp{(g~)il that in conditions hold, will be denoted by ~'.

2) with z = ~(x) that on dynamics strongly dynamics that (AI) for 0 (see has that, and with A(x) constant a has static degrees row on O. 4). full dimension f:- f + g~ system Section that the relative that ~ to decouplable matrix (~,~) e ~(& ) such general the decoupling C0, [vdS2]). 10) input-output holds the £ n C - sp{~ . . 12) Zi+ 2 - (h i L~h i ... ~i-lhl)T , Then the system ^ ~ fl(zl ..... z2÷2) + ^ za i = i ..... 1,2) has the form ^ zl ^ ..... z2+z)vl + gla(zl ..... z~+2)v ^ -- f a ( z 2 .

### A Boundary Control Problem for a Nonlinear Parabolic Equation by Maksimov V. I.

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