LMI-Based Computation of the Instability Measure of Continuous-Time Linear Systems with a Scalar Parameter

Abstract

Measuring the instability is a fundamental issue in control systems. This paper investigates the instability measure defined as the sum of the real parts of the unstable eigenvalues, which has important applications such as stabilization with information constraint. We consider continuous-time linear systems whose coefficients are linear functions of a scalar parameter constrained into an interval. The problem is to determine the largest instability measure for all admissible values of the parameter. Two sufficient and necessary conditions for establishing upper bounds on the sought instability measure are proposed in terms of linear matrix inequality (LMI) feasibility tests. The first condition exploits Lyapunov functions, while the second condition is based on the determinants of some specific matrices. Some numerical examples are used to compare the proposed conditions.