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A linear, finite‐dimensional plant, with state‐space parameter dependence, is controlled using a parameter‐dependent controller. The parameters whose values are in a compact set, are known in real time. Their rates of variation are bounded and known in real time also. The goal of control is to stabilize the parameter‐dependent closed‐loop system, and provide disturbance/error attenuation as measured in induced L2 norm. Our approach uses a bounding technique based on a parameter‐dependent Lyapunov function, and then solves the control synthesis problem by reformulating the existence conditions into a semi‐infinite dimensional convex optimization. We propose finite dimensional approximations to get sufficient conditions for successful controller design.

The earliest evidence for subduction, which could have been localized, does not signify when plate tectonics became a global phenomenon. To test the antiquity of global subduction, we investigated Paleoproterozoic time, for which seismic evidence is available from multiple continents. We used a new high-density seismic array in North China to image the crustal structure that exhibits a dipping Moho bearing close resemblance to that of the modern Himalaya. The relict collisional zone is Paleoproterozoic in age and implies subduction operating at least as early as ~2 billion years (Ga) ago. Seismic evidence of subduction from six continents at this age is interpreted as the oldest evidence of global plate tectonics. The sutures identified can be linked in a plate network that resulted in the assembly of Nuna, likely Earth’s first supercontinent. Global subduction by ~2 Ga ago can explain why secular planetary cooling was not appreciable until Proterozoic time.

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