Robust triangular decoupling via output feedback (Q5950731)

The authors consider the case of linear systems with nonlinear uncertain structure: NEWLINE\[NEWLINE\dot x(t) = A(q)x(t) + B(q)u(t),\quad y(t) = C(q)x(t),NEWLINE\]NEWLINE where \(x\in\mathbb R^n\) is the state vector, \(u\in\mathbb R^m\) is the input vector and \(y\in\mathbb R^p\) is the output vector. The matrices \(A(q)\in[\wp(q)]^{n\times n}\), \(B(q)\in[\wp(q)]^{n\times m}\), \(C(q)\in[\wp(q)]^{p\times n}\) are function matrices depending upon the uncertainty vector \(q = [q_1,\dots, q_l]\in\mathbb Q\) (\(\mathbb Q\) denotes the uncertain domain). The set \(\wp(q)\) is the set of nonlinear functions of \(q\). The uncertainties \(q_1,\dots,q_l\) do not depend upon time. For the nonlinear structure of the system matrices \(A(q)\), \(B(q)\) and \(C(q)\), no limitations or specifications (continuity, boundedness, smoothness, etc.) are required. Using an output feedback controller independent of the uncertainties, the following facts are established: necessary and sufficient conditions for the robust triangular decoupling problem to have a solution, the general analytical expression of output feedback matrices independent of the uncertainties and the general form of the triangularly decoupled closed-loop system, facilitating the derivation of sufficient conditions for simultaneous robust stability.