Robust stabilization and enlargement of attractive region of control systems using piecewise linear Lyapunov functions

The purpose of this paper is to present a method to design control gain matrices by using piecewise linear Lyapunov functions so that closed systems are robust stable and attractive regions are as large as possible in given polytopic regions. The design problems for these specifications are formulated as bilinear minimization problems whose variables are parameters included in piecewise linear Lyapunov functions and control gain matrices. The main result of this paper is to propose a method to solve bilinear programming problems so that the objective value at the obtained solution is in an ε neighborhood of the global optimal value.