A less conservative approach to handle time‐varying parameters in discrete‐time linear parameter‐varying systems with applications in networked control systems

Abstract

SummaryThis article proposes a new strategy to deal with linear parameter‐varying discrete‐time systems, whose time‐varying parameters can be written as solutions (such as exponential, trigonometric, or periodic function) of a linear difference equation (DE). The novelty is to explicitly exploit the precise knowledge of the function describing the time‐varying parameter by incorporating the associated DE in the conditions, providing less conservative results when compared with conventional approaches based on bounded or arbitrary rates of variation. The advantage of the method comes from the fact that, differently from the available methods, the pointwise stability for the whole domain of the time‐varying parameters is not a necessary condition to obtain feasible solutions. The applicability and benefits of the proposed technique are investigated in terms of numerical examples concerning robust stability analysis, filtering, and state‐feedback control. As a final contribution, the problem of time‐varying sampling periods in the context of networked control systems is investigated using the proposed strategy. A numerical example based on a practical application is presented to illustrate the superiority of the approach when compared to methods from the literature based on matrix exponential computation.

Stabilization and disturbance rejection with decay rate bounding in discrete‐time linear parameter‐varying systems via ℋ∞gain‐scheduling static output feedback control

“…also holds. Now, following the idea depicted in Mehdi et al, 37 we can pre-and post-multiply (21) by…”

“…Therefore, with V(x(k)) being a parameter-dependent Lyapunov function, the feasibility of ( 16), (17), and ( 20) is sufficient to ensure (21), and consequently (31). Thus, the asymptotic stability of ( 5) is guaranteed with decay rate bounded by 𝜌 sof , for any arbitrary variation of the time-varying parameters in the system polytope.…”

“…19 Recently, a more general proposal of linear matrix inequalities (LMI) conditions for the synthesis of GS ℋ ∞ controller emerged, 20 along with a new approach based on the case where the time-varying parameters can be written as solutions of a linear difference equation. 21 A particular approach which has been intensively investigated is the use of homogeneous polynomial parameter-dependent Lyapunov functions (HPPDLF). Analysis and control synthesis conditions were presented for state-feedback control, using HPPDLF and multi-affine Lyapunov functions.…”

Iterative Solution of Linear Matrix Inequalities for the Combined Control and Observer Design of Systems with Polytopic Parameter Uncertainty and Stochastic Noise

“…In addition, notice that the obtained solution can be conservative due to the use of a common quadratic Lyapunov function for the whole polytope. The use of parameter-dependent Lyapunov functions, such as those discussed in [29] for discrete-time processes with time-varying parameters, will be a subject of future research.…”

Robust Static Output-Feedback Control for MJLS with Non-Homogeneous Markov Chains: A Comparative Study Considering a Wireless Sensor Network with Time-Varying PER

“…The most recent research in the WSN literature is concerned with improving the robustness of the network by using, for instance, topology optimization models to help WSN resist cascading failures [ 2 , 3 ], information fusion processes to lower the negative impact of the environment on message routing [ 4 ], and more realistic failure models to analyse the network invulnerability [ 5 ]; etc. However, if the network is used as a communication channel for NCS projects, there are some alternative techniques that guarantee the robustness of the closed-loop system even under, for instance, denial of service in cyber-physical attacks [ 6 , 7 ], network-induced delays [ 8 ], and packet loss, among several other issues [ 9 , 10 , 11 ]. In this sense, despite their advantages, the most common and least wanted feature of the NCS is the possibility of packet loss in the network.…”