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In this technical note, we generalize the well-known Lyapunov-basedstabilizability and detectability tests for linear time-invariant (LTI) systemsto the context of discrete-time (DT) polytopic linear parameter-varying (LPV)systems. To do so, we exploit the mathematical structure of the class ofpoly-quadratic Lyapunov functions, which enables us to formulate conditions inthe form of linear matrix inequalities (LMIs). Our results differ from existingconditions in that we adopt weaker assumptions on the parameter dependence ofthe controllers/observers and our method does not require explicitlyincorporating these gains, which renders the new conditions lesscomputationally demanding. Interestingly, our results also have importantimplications for existing controller and observer synthesis techniques based onpoly-QLFs. In fact, we show that existing observer synthesis results arestronger than was anticipated in the sense that they are necessary for a largerclass of observers. Moreover, we also introduce new controller synthesisconditions and illustrate our results by means of a numerical case study.

Efficient Lyapunov-Based Stabilizability and Detectability Tests: From LTI to LPV Systems