Exact prescribed-time stabilization and observer design for a class of MIMO nonlinear systems

This paper addresses the problems of exact prescribed-time stabilization and observer design for a class of multi-input-multi-output (MIMO) nonlinear systems. By introducing the concept of left and right clustered matrices and exploring their properties, solutions to two classes of parametric Lyapunov equations (PLEs) associated with the coefficients of the linear part of the MIMO nonlinear systems are thoroughly investigated. These two PLEs are then utilized as the key tool to solve respectively the exact prescribed-time stabilization of the MIMO nonlinear system where the nonlinear functions satisfy a linear growth condition with unknown coefficients, and the exact prescribed-time observer design of the MIMO nonlinear system where the nonlinear functions are known and satisfy the Lipschitz condition. The approach is also extended to solve the problem of prescribed-time stabilization of a class of MIMO nonlinear systems by observer-based output feedback. Finally, two numerical examples demonstrate the effectiveness of the proposed approaches.