  We propose a new matrix pencil based approach for design of state-feedback
and output-feedback stabilizing controllers for a general class of uncertain
nonlinear strict-feedback-like systems. While the dynamic controller structure
is based on the dual dynamic high-gain scaling based approach, 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 dynamic controller are extracted in
terms of generalized eigenvalues associated with matrix pencils formulated to
capture the detailed structures (locations of uncertain terms in the system
dynamics and their state dependences) of bounds in the Lyapunov analysis. The
proposed approach enables efficient computation of non-conservative bounds with
reduced algebraic complexity and enhances feasibility of application of the
dual dynamic high-gain scaling based control designs. The proposed approach is
developed under both the state-feedback and output-feedback cases and the
efficacy of the approach is demonstrated through simulation studies on a
numerical example.
