Efficient non-conservative realization of dynamic scaling-based controllers via matrix pencils for uncertain nonlinear strict-feedback systems

We propose a new matrix pencil based approach for design of state-feedback and output-feedback controllers for uncertain nonlinear strict-feedback-like systems. While the dynamic controller structure is based on dynamic high-gain scaling, we cast the design procedure within a general matrix pencil structure unlike prior results that utilized conservative algebraic bounds of terms arising in Lyapunov inequalities. The design freedoms in the controller are extracted in terms of generalized eigenvalues associated with matrix pencils formulated to capture detailed structures (locations and state dependences) of uncertain terms in the system dynamics. The approach is developed under both state-feedback (dynamic high-gain scaling based controller) and output-feedback (dual dynamic high-gain scaling based controller and observer) cases and is shown to enable efficient computation of non-conservative bounds with reduced algebraic complexity. The efficacy of the approach is demonstrated through simulation studies.