access icon free Robust sampled-data control of non-linear LPV systems: time-dependent functional approach

This study addresses the problem of robust exponential stability and stabilisation of sampled-data linear parameter varying (LPV) systems with an aperiodic sampling rate. Utilising the input delay approach and taking the distance between real and measured parameters into account, new stability and stabilisation conditions are derived for LPV systems with arbitrary dependence on the parameters. By means of a modified parameter dependent Lyapunov–Krasovskii functional, stability conditions are formulated as a set of parameter-dependent linear matrix inequalities (PLMIs) which are suitable to investigate the effect of the sampling rate on the closed-loop stability. Furthermore, sufficient conditions to guarantee the feasibility of PLMIs over the set of whole parameters are derived that lead to the feasibility of a finite number of linear matrix inequalities. Applying the projection lemma new stability analysis conditions are obtained and shown to be suitable for the stabilisation problem. Under the new stability criteria, an efficient procedure developed for robust sampled-data controller design in the presence of uncertainty on the varying parameters and unknown time varying sampling rate. The proposed method is applied to a sampled-data fuzzy control problem of a non-linear system and multi-rate sampled-data LPV systems. Several examples show the efficiency of the method.

Inspec keywords: asymptotic stability; matrix algebra; fuzzy control; uncertain systems; time-varying systems; linear matrix inequalities; stability; delays; control system synthesis; nonlinear control systems; continuous time systems; control system analysis; closed loop systems; linear systems; robust control; sampled data systems; Lyapunov methods

Other keywords: aperiodic sampling rate; stabilisation conditions; parameter-dependent linear matrix inequalities; time-dependent functional approach; arbitrary dependence; closed-loop stability; stability conditions; robust sampled-data controller design; sampled-data LPV systems; robust exponential stability; nonlinear LPV systems; input delay approach; sufficient conditions; parameters variation rate; stabilisation problem; robust sampled-data control; sampled-data fuzzy control problem; sampled-data linear parameter-varying systems; varying parameters; modified parameter; stability analysis conditions; measured parameters

Subjects: Nonlinear control systems; Control system analysis and synthesis methods; Algebra; Distributed parameter control systems; Time-varying control systems; Discrete control systems; Stability in control theory

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