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# Sampled-data integral control of multivariable linear infinite-dimensional systems with input nonlinearities

• * Corresponding author: Chris Guiver
• A low-gain integral controller with anti-windup component is presented for exponentially stable, linear, discrete-time, infinite-dimensional control systems subject to input nonlinearities and external disturbances. We derive a disturbance-to-state stability result which, in particular, guarantees that the tracking error converges to zero in the absence of disturbances. The discrete-time result is then used in the context of sampled-data low-gain integral control of stable well-posed linear infinite-dimensional systems with input nonlinearities. The sampled-date control scheme is applied to two examples (including sampled-data control of a heat equation on a square) which are discussed in some detail.

Mathematics Subject Classification: Primary: 93C05, 93C10, 93C25, 93C35, 93C55, 93C57, 93D09, 93D15; Secondary: 93C20.

 Citation: • • Figure 4.1.  Quantization function $q_\delta$

Figure 4.2.  Square domain $\Omega \subseteq \mathbb R^2$

Figure 4.3.  Feasible sets of reference vectors $r = {\left( {\begin{array}{*{20}{l}} {{r_1}}&{{r_2}} \end{array}} \right)^T}$ for $\phi_1$ (darker grey) and $\phi_2$ (lighter gray) regions. The reference $r$ in (4.8) is marked with a cross

Figure 4.4.  Model data as in (4.5), (4.6), (4.8) and (4.9). (a) Initial temperature profile $z^0$. (b) Temperature profile of solution $z$ at time $t = 20$. (c) Outputs. (d) Held inputs. In panels (c) and (d), the solid and dashed lines correspond to $\tau = 0.25$ and $\tau = 0.5$, respectively. The dotted lines in panel (c) are the components of the reference

Figure 4.5.  Model data as in (4.5), (4.6), (4.8), (4.10) and (4.11). (a) Outputs. (b) Held inputs. In panels (a) and (b), the solid and dashed lines correspond to the external forcing $v$ and $3 v$, respectively. The dotted lines in panel (a) are the components of the reference

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