Dynamic $L_{\text{2}}$ Output Feedback Stabilization of LPV Systems With Piecewise Constant Parameters Subject to Spontaneous Poissonian Jumps

Abstract

This letter addresses the L 2 output feedback stabilization of linear parameter varying systems, where the parameters are assumed to be stochastic piecewise constants under spontaneous Poissonian jumps. We provide sufficient conditions in terms of linear matrix inequalities (LMIs) for the existence of a full-order output feedback controller. Such LMIs, however, can be computationally intractable due to the presence of integral terms. Nevertheless, we show that these LMIs can be equivalently represented by an integral-free LMI, which is computationally tractable. Finally, we provide analytical formulas to construct the controller and illustrate the applicability of the results through examples.

Distributed output feedback control of decomposable LPV systems with delay and switching topology: application to consensus problem in multi-agent systems

“…To demonstrate the efficacy of our result, we applied it to consensus problem of multi-agent systems under parameter varying delay and switching topology. Many extensions of our result can be expected; for instance, extension to other families of distributed systems and coordination patterns, and extension to the case where the pattern matrix and parameter variation are stochastic following the ideas of Briat (2018) and Zakwan (2020).…”

“…C 12 = C 11 , D 11 = 0 6×5 , ρ) = 0.0670 + 0.4390ρ, a 34 (ρ) = 0.0479 + 2.3440ρ, b 21 (ρ) = 0.9263 + 4.0760ρ,and the parameter ρ ∈ [0 1] is defined as ρ = 0.0091(θ t − 60), where θ t ∈ [60 170] is the airspeed in knots. This example is inspired byZakwan (2020).Remark 4.1: Note that the output matrices C 21 and C 22 have incomplete row rank.…”

Dynamic output feedback control of delayed linear parameter varying systems with piecewise constant parameters: A clock‐dependent L–K approach

“…In this section, we illustrate the efficacy of our result by applying it to VTOL helicopter model introduced in References 20,25,43 . The dynamics of the system can be given as where is a time‐varying parameter and the state variables are horizontal velocity, the vertical velocity, the pitch rate, and the pitch angle, respectively.…”

“…LPV systems with piecewise constant parameters also arise naturally in synchronous buck converters with piecewise constant loads 18 and as a simplifying assumption in the control of LPV sampled‐data systems 19 . In the stochastic framework, LPV systems with piecewise constant parameters have been discussed in References 16 and 20. As the class of LPV systems with piecewise constant parameters is closely related to the class of switched systems, it seems natural to use tools developed for switched systems 21,22 to obtain sufficient stability conditions for such LPV systems by introducing dwell‐time constraints.…”

Dwell-Time Based Stability Analysis and L2 Control of LPV Systems with Piecewise Constant Parameters and Delay

“…LPV systems with piecewise constant parameters arise naturally in the context of sampled-data control of LPV systems (Joo and Kim (2015)) and control of buck converters with piecewise constant loads (Tan et al (2002)). LPV systems with piecewise constant parameters can be considered as switched systems with an uncountable number of modes in a bounded compact set, Zakwan (2020). LPV systems with piecewise constant parameters subject to spontaneous Poissonian jumps are also discussed in Briat (2018) and Zakwan (2020).…”