An LMI approach to H∞H∞ boundary control of semilinear parabolic and hyperbolic systems

Exponential stability analysis and L2L2-gain analysis are developed for scalar uncertain distributed parameter systems, governed by semilinear partial differential equations of parabolic and hyperbolic types. Sufficient exponential stability conditions with a given decay rate are derived in the form of Linear Matrix Inequalities (LMIs) for both systems. These conditions are then utilized to synthesize H∞H∞ static output feedback boundary controllers of the systems in question.