Brief paper: Non-conservative matrix inequality conditions for stability/stabilizability of linear differential inclusions

Authors:
Tingshu Hu;Franco Blanchini
Affiliations:
Department of Electrical and Computer Engineering, University of Massachusetts, Lowell, MA 01854, United States;Dipartimento di Matematica e Informatica, Universití degli Studi di Udine, Via delle Scienze 208, 33100 Udine, Italy
Venue:
Automatica (Journal of IFAC)
Year:
2010

Citing 8
Cited 1

Criteria of asymptotic stability of differential and difference inclusions encountered in control theory

Systems & Control Letters
Constrained regulation of linear continuous-time dynamical systems

Systems & Control Letters
Nonquadratic Lyapunov functions for robust control

Automatica (Journal of IFAC)
Piecewise Lyapunov functions for robust stability of linear time-varying systems

Systems & Control Letters
Brief paper: Nonlinear control design for linear differential inclusions via convex hull of quadratics

Automatica (Journal of IFAC)
Survey paper: Set invariance in control

Automatica (Journal of IFAC)
Brief On absolute stability analysis by polyhedral Lyapunov functions

Automatica (Journal of IFAC)
Brief Homogeneous Lyapunov functions for systems with structured uncertainties

Automatica (Journal of IFAC)

A new class of Lyapunov functions for the constrained stabilization of linear systems

Automatica (Journal of IFAC)

Quantified Score

Hi-index	22.16

Visualization

Abstract

This paper shows that the matrix inequality conditions for stability/stabilizability of linear differential inclusions derived from two classes of composite quadratic functions are not conservative. It is established that the existing stability/stabilizability conditions by means of polyhedral functions and based on matrix equalities are equivalent to the matrix inequality conditions. This implies that the composite quadratic functions are universal for robust, possibly constrained, stabilization problems of linear differential inclusions. In particular, a linear differential inclusion is stable (stabilizable with/without constraints) iff it admits a Lyapunov (control Lyapunov) function in these classes. Examples demonstrate that the polyhedral functions can be much more complex than the composite quadratic functions, to confirm the stability/stabilizability of the same system.