On Input-to-State Stability of Homogeneous Evolution Equations

Abstract: Homogeneity is a symmetry of an object with respect to a dilatation. All linear and many nonlinear models of mathematical physics are homogeneous. For example, Burgers, KdV and Navier-Stokes equations are symmetric with respect to a properly selected dilation. Finite dimensional homogeneous control systems are known to be similar with linear ones, but they may have a better regulation quality like a faster convergence, stronger robustness and less overshoot. This talk is devoted to Input-to-State Stability analysis of homogeneous evolution equations in Banach spaces. Similarly to the finite-time dimensional case, it is shown that the uniform asymptotic stability of homogeneous unperturbed system guarantees its Input-to-State Stability with respect to homogeneously involved perturbations.

systems and controlanalysis of PDEsclassical analysis and ODEsdynamical systemsoptimization and control

Audience: researchers in the topic

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Input-to-State Stability and its Applications

Series comments: This is a seminar for the exchange of ideas in input-to-state stability (ISS) theory and related fields.

The scope of the Seminar includes but is not limited to

- ISS for finite-dimensional systems (ODEs, hybrid, impulsive, switched, discrete-time systems),

- Infinite-dimensional ISS theory (PDEs, evolution equations in Banach spaces, time-delay systems, infinite networks)

- Applications to robust control and observation, nonlinear control, network analysis, etc.

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