Nonquadratic Lyapunov functions for robust control
Automatica (Journal of IFAC)
Piecewise Lyapunov functions for robust stability of linear time-varying systems
Systems & Control Letters
A Convex Approach to Robust Stability for Linear Systems with Uncertain Scalar Parameters
SIAM Journal on Control and Optimization
Brief Homogeneous Lyapunov functions for systems with structured uncertainties
Automatica (Journal of IFAC)
Stability analysis of uncertain genetic sum regulatory networks
Automatica (Journal of IFAC)
Automatica (Journal of IFAC)
Visual servoing path planning via homogeneous forms and LMI optimizations
IEEE Transactions on Robotics
Convex relaxations in circuits, systems, and control
IEEE Circuits and Systems Magazine
IEEE Transactions on Fuzzy Systems
Generalized nonquadratic stability of continuous-time Takagi-Sugeno models
IEEE Transactions on Fuzzy Systems
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This paper deals with robust stability analysis of linear state space systems affected by time-varying uncertainties with bounded variation rate. A new class of parameter-dependent Lyapunov functions is introduced, whose main feature is that the dependence on the uncertain parameters and the state variables are both expressed as polynomial homogeneous forms. This class of Lyapunov functions generalizes those successfully employed in the special cases of unbounded variation rates and time-invariant perturbations. The main result of the paper is a sufficient condition to determine the sought Lyapunov function, which amounts to solving an LMI feasibility problem, derived via a suitable parameterization of polynomial homogeneous forms. Moreover, lower bounds on the maximum variation rate for which robust stability of the system is preserved, are shown to be computable in terms of generalized eigenvalue problems. Numerical examples are provided to illustrate how the proposed approach compares with other techniques available in the literature.