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 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)
Sliding mode control for polytopic differential inclusion systems
Mathematics and Computers in Simulation
Robust stabilization of linear differential inclusion system with time delay
Mathematics and Computers in Simulation
Mathematics and Computers in Simulation
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This paper presents a nonlinear control design method for robust stabilization and robust performance of linear differential inclusions (LDIs). A recently introduced non-quadratic Lyapunov function, the convex hull of quadratics, will be used for the construction of nonlinear state feedback laws. Design objectives include stabilization with maximal convergence rate, disturbance rejection with minimal reachable set and least L"2 gain. Conditions for stabilization and performances are derived in terms of bilinear matrix inequalities (BMIs), which cover the existing linear matrix inequality (LMI) conditions as special cases. Numerical examples demonstrate the advantages of using nonlinear feedback control over linear feedback control for LDIs. It is also observed through numerical computation that nonlinear control strategies help to reduce control effort substantially.