Stability and performance analysis of hybrid integrator–gain systems: A linear matrix inequality approach

Hybrid integrator–gain systems (HIGS) are nonlinear elements designed for overcoming fundamental limitations of linear time-invariant integrators. This paper presents numerically robust conditions time-domain stability and performance HIGS-controlled systems. In particular, using piecewise quadratic (PWQ) Lyapunov functions defined over polyhedral subregions the state-space, computations upper-bounds on L2-gain H2-norm formulated as convex optimization problems in terms tractable matrix inequalities (LMIs). order to improve accuracy robustness, LMIs constructed a manner eliminate explicit equality constraints typically related continuity PWQ functions. Novel presented that guide further refinement which increase approach. The effectiveness analysis tools is demonstrated through numerical case-study motion system.