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This paper employs the observer-based output feedback control technique to deal with the problem of spatiotemporally asynchronous sampled-data control for a linear parabolic PDE on a hypercube. By the spatiotemporally asynchronous sampled-data observation outputs, an observer-based output feedback control law is constructed, where the sampling interval in time is bounded. By constructing an appropriate Lyapunov–Krasovskii functional candidate and applying a weighted Poincaré–Wirtinger inequality on a hypercube, it is shown under a sufficient condition presented in terms of standard linear matrix inequalities that the suggested spatiotemporally asynchronous sampled-data control law asymptotically stabilises the PDE in the spatial H 1 (Ω) norm but its convergence speed can be regulated by a known constant. Moreover, both open-loop and closed-loop well-posedness analysis are done within the framework of C 0 semi-group. Finally, numerical simulation results are presented to support the proposed design method. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of dynamic compensator design for exponential stabilisation of linear parabolic partial differential equations (PDEs) with multiple actuation control inputs and multiple non-collocated observation outputs. Both in-domain control and boundary control are considered. A new observer-based dynamic compensator is constructed by the non-collocated observation outputs such that the resulting closed-loop coupled PDEs are exponentially stable. By constructing a Lyapunov function candidate and using Poincaré–Wirtinger inequality's variants, a sufficient condition for the existence of such dynamic compensator is presented in terms of standard linear matrix inequalities (LMIs). The closed-loop well-posedness analysis result is also established by the method of C 0 -semigroup and its perturbations by bounded/unbounded linear operators. Finally, numerical simulation results are presented to support the proposed design method. [ABSTRACT FROM AUTHOR]

This paper discusses the design problem of distributedH∞Luenberger-type partial differential equation (PDE) observer for state estimation of a linear unstable parabolic distributed parameter system (DPS) with external disturbance and measurement disturbance. Both pointwise measurement in space and local piecewise uniform measurement in space are considered; that is, sensors are only active at some specified points or applied at part thereof of the spatial domain. The spatial domain is decomposed into multiple subdomains according to the location of the sensors such that only one sensor is located at each subdomain. By using Lyapunov technique, Wirtinger's inequality at each subdomain, and integration by parts, a Lyapunov-based design of Luenberger-type PDE observer is developed such that the resulting estimation error system is exponentially stable with anH∞performance constraint, and presented in terms of standard linear matrix inequalities (LMIs). For the case of local piecewise uniform measurement in space, the first mean value theorem for integrals is utilised in the observer design development. Moreover, the problem of optimalH∞observer design is also addressed in the sense of minimising the attenuation level. Numerical simulation results are presented to show the satisfactory performance of the proposed design method. [ABSTRACT FROM PUBLISHER]

This paper deals with the problem of static output feedback (SOF) control design for a class of diffusion partial differential equation (PDE) and ordinary differential equation (ODE) cascades, where the ODE model is used to describe the dynamics of the multi-input and multi-output (MIMO) plant and the diffusion PDE model is employed to represent the dynamics of actuators. The objective of this paper is to develop a simple as well as effective SOF controller via the Lyapunov's direct method such that the resulting closed-loop system is globally exponentially stable. By constructing a quadratic Lyapunov function, the sufficient condition on the globally exponential stability of the closed-loop cascaded system is presented in terms of linear matrix inequality (LMI). Then, an LMI-based design method of the SOF controller is developed on the basis of the obtained stability analysis result. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed design method. [ABSTRACT FROM PUBLISHER]