Analysis and synthesis of robust stability for linear time-invariant descriptor systems (Q2744502)

The authors discuss the problems of robust stability analysis and synthesis for linear time-invariant systems NEWLINE\[NEWLINEE{dx\over dt}= Ax,\tag{\(*\)}NEWLINE\]NEWLINE NEWLINE\[NEWLINEE{dx\over dt}= (A+\Delta A) x,\tag{\(**\)}NEWLINE\]NEWLINE NEWLINE\[NEWLINEE{dx\over dt}= Ax+ Bu,\tag{\(***\)}NEWLINE\]NEWLINE where \(x\) is a state vector; \(E\) and \(A\) are \(n\times n\)-matrices; \(\Delta A\) is a perturbation matrix of \(A\); \(u\) is an \(m\)-input vector and \(B\) is an \(n\times m\) matrix. Based on the results arising from a Lyapunov equation and a Riccati equation associated to the systems, the stability analysis for the linear system \((*)\), the robust stability analysis and robust stability methods for systems \((**)\) and \((***)\) are proposed, respectively.