Impulse Analysis of Linear Time-Varying Singular Systems

Controllability and observability for time‐varying switched impulsive controlled systems

“…Guan et al [22] investigated the sufficient and necessary conditions for state controllability and observability of linear time-varying impulsive systems. And Yan and Duan [26] studied the impulsive controllability and impulsive observability for linear timevarying singular system.…”

Consistent‐inconsistent decomposition to initial value problem of descriptor linear systems

“…where N (t) and B(t) are infinitely differentiable matrix-value function on R, and N (t) is strictly upper triangular for all t. For more detail see [3,9]. As before, the control input u is assumed to be a sufficiently smooth function mapping R + = [0, +∞) to R r , and the initial value x 0 ∈ R n is arbitrary.…”

“…Descriptor systems (singular systems, differential-algebraic equations) are an interesting research topic in numerical mathematics, mechanics, and control theory recently [1][2][3][4][5][6][7][8][9]. Among many interesting phenomena, we point out the inconsistent initial value problem, which results in, for example, the need for reinitialization in numerical integration [6] and impulse elimination in control [2] for this type of systems.…”

An Adaptive Soft Sensor Based on Nonlinear Differential-Algebraic Observer for Chemical Processes

“…In some chemical processes, the dynamic responses of some variables are much faster than others, hence, the former can be assumed as quasi-steady-state, and some differential equations will become algebraic equations to form a differential-algebraic system. In the past two decades, they have been widely studied, including stability and Lyapunov theorem [14], poles assignment [15], state feedback stabilization [16], impulse analysis [17], observability and controllability [18][19][20], most of which focus on linear differential-algebraic systems or a specific class of nonlinear differential-algebraic systems.…”