A criterion of absolute stability of nonlinear sampled-data control systems in the form of numerical procedures (Q581336)

Through an iterative procedure involving the solution of an eigenvalue min-max condition at the M vertices of a closed convex polyhedron \(P\subset R^ m\) and testing the validity of at most M matrix equations, the authors show that the zero solution of the discrete-time control problem \[ (1)\quad x(s+1)=[A+\sum^{m}_{i=1}k_ iu_ i(s)A_ i)]x(s),\quad s=0,1,2,... \] will be uniformly asymptotically stable for all control vectors \(u\in P\), where \(x\in R^ n\), A, \(A_ i\) are constant square matrices, and the \(k_ i\) are constants. Furthermore, if the \(k_ i\) are parameters, then the determination of a region U in parameter space for which (1) is uniformly asymptotically stable for all \(u\in P\) is formulated in terms of a mathematical programming problem. An example is given.