Two side observer design for singular distributed parameter systems

L2 norm-based finite-time stability and boundedness of singular distributed parameter systems with parabolic type

“…Meanwhile, it can describe a wide family of problems in practical applications, including the transdermal application of drugs, the temperature description of the multi-functional office building and so on, which has been extensively studied. 3,17 For example, as a model for the building temperature control, the distributed air conditioning is implemented to achieve collaborative energy and thermal optimal management in the work by Y Jiang et al 3 To facilitate the analysis, the assumptions and definitions are given as follows.…”

“…In views of different temperature preferences, the distributed air conditioning is implemented to achieve collaborative energy and thermal optimal management. 3 And the distributed air conditioning system consists of two operating subsystems, one is the cooling system driven by deep wells pumps, and another is the solar radiation sensor heating system that is implemented in the window glass. Suppose that the horizontal dimension of the solar collector is much more than the vertical size and the coupling is only affected between two adjacent floors.…”

“…Based on the semi-group theory in Hilbert space, the exponential stability of the first-order SDPSs was concerned, and the sufficient conditions were derived in the work by Ge et al 18 Most of the existing studies have been done on the system Lyapunov asymptotic stability, which describes the asymptotic behavior of the state trajectory as time approaches infinity. 3,10,12 However, in many practical applications, the primary attention may be paid to the transient response of the systems within a specified time interval. 19,20 In this case, finite-time stability could be used.…”

“…Singular distributed parameter systems (SDPSs), which governed by partial differential equations with singular matrix coefficient, are derived from the study of industrial distributed processes and physical phenomena under simplified assumptions such as the design of electronic circuits, 1 biological, economic models and one-dimensional (1D) drift-diffusion equation.. 2–4 The real world has provided a profound practical research background for SDPSs, such as involved in the fields of nanoelectronics, mechanical engineering, and electric networks. 5 The SDPS not only yields time-dependent systems of algebraic differential equations but also exhibits the spatial physical effects described by partial differential equations in space or time/space.…”

“…First, up to now, most of the current references that tackle the stability of partial differential equations PDEs-based systems are mainly focused on the asymptotic stability, which is defined on an infinite time interval. 3,10,12,14,18 Second, many industrial and engineering processes can be governed by coupled partial differential equations with singular matrix coefficients, and the SDPSs have been of interest from a practical viewpoint. 1–5 Third, to the best of the authors’ knowledge, results on the control problem of FT stability and FT boundedness for SDPSs with parabolic type have not been investigated in the literature yet.…”