We consider the design of state feedback control laws for both the switching signal and the continuous input of an unknown switched linear system, given past noisy input-state trajectories measurements. Based on Lyapunov–Metzler inequalities and on a matrix S-lemma, we derive data-dependent bilinear programs, whose solution directly returns a provably stabilizing controller and ensures H₂ or H_∞ performance. We further present relaxations that considerably reduce the computational cost, still without requiring stabilizability of any of the switching modes. Finally, we showcase the flexibility of our approach on the constrained stabilization problem for an unknown perturbed linear system. We validate our theoretical findings numerically, demonstrating the favorable trade-off between conservatism and tractability achieved by the proposed relaxations.

Scholars and practitioners acknowledge the role of design, and specifically design thinking, as a driver of innovation and change. Design thinking is gaining attention in the business community beyond the traditional product innovation realm and is increasingly promoted as an engine for the creation of novel user experiences, new businesses, strategic transformation, organizational and cultural change. Is it reasonable to assume that the same set of practices fits such a broad range of applications equally well? This study addresses how design thinking applications are differently framed when addressing diverse innovation purposes. Specifically, we compare two purposes: innovation of solutions, encompassing traditional product and service development projects, and innovation of direction, encompassing strategic and organizational renewal projects. Based on data collected from 146 design thinking projects conducted by European consulting firms we investigate the relationships between the design thinking practices adopted and the value generated by the projects. We then analyze how these relationships vary depending on the purpose of the innovation project, namely whether focused on innovating solutions or direction. The results show that different purposes indeed call for different practices. In projects aimed at innovating solutions, market value is positively related to capturing current user needs and envisioning future society. Conversely, in projects aimed at innovating direction, market value is positively related to challenging current assumptions.