H∞ boundary control of semilinear heat processes and distributed mechanical oscillators: An LMI approach

Exponential stability analysis and L₂-gain analysis are developed for uncertain distributed parameter systems. Scalar heat processes and distributed mechanical oscillators, governed by semilinear partial differential equations of parabolic and, respectively, hyperbolic types, are chosen for treatment. Sufficient exponential stability conditions with a given decay rate are derived in the form of linear matrix inequalities (LMIs) for an uncertain heat conduction equation and for an uncertain wave equation. These conditions are then utilized to synthesize H_{spl infin/} static output-feedback boundary controllers of the systems in question.