A team algorithm for robust stability analysis and control design of certain time-varying linear systems using piecewise quadratic Lyapunov functions (Q2716778)

Two problems are considered: a) given the system NEWLINE\[NEWLINE\dot x= (A_0+\delta E(t)) x,\quad t\geq 0NEWLINE\]NEWLINE with \(E(t)\in \Omega_E\subset \mathbb{R}^n\), \(\Omega_E\) being a polytope, \(A_0\) a Hurwitz matrix, find the maximal \(\delta\geq 0\) such that asymptotic stability is preserved, b) given NEWLINE\[NEWLINE\dot x= (A_0(k)+ \delta E(k, t)) xNEWLINE\]NEWLINE with \(E(t)\in \Omega_E\), find the optimal value of the parameter vector \(k\) that maximizes \(\delta\geq 0\) of the previous problem. The two problems are solved by decomposition in some convex subproblems for certain subsets of decision variables. Three examples are given.