Spectral Approach for Time–Invariant Systems with General Spatial Domain

摘要: The spectral analysis of a finite– or infinite–dimensional linear operator is well–established and profound mathematical tool for stability feedback control design. dynamic system properties are thereby determined based on the eigenvalue distribution respective set eigenvectors. For systems governed by PDEs certain restrictions apply, which in particular related to possible existence continuous spectra. Fortunately, wide class physically important including, e.g., diffusion–convection–reaction, wave, Euler–Bernoulli, Timoshenko beam equations, yields so–called Riesz operators, exhibit purely discrete whose eigenvectors adjoint eigenvectors, respectively, span basis underlying function space. These can be advantageously exploited controllability observability similar finite–dimensional case [14]. Furthermore, operators satisfy spectrum growth assumption such that directly [14, 37]. This property utilized stabilizability as well design stabilizing state–feedback controllers, see, [65, 33, 13, 48, 49, 37] references therein.