Linear State‐Space Control Systems

Linear Mathematical Model for State-Space Representation of Small Scale Turbojet Engine with Variable Exhaust Nozzle

“…Based on the proof by Williams and Lawrence (2007), one can substitute the nonlinear functions f [x(t), u(t), t] and h [x(t), u(t), t] of (1) with their multivariable Taylor series around the selected operational point described by [x 0 (t), u 0 (t), t]. Supposing the state, input and output all remain in the vicinity of their respective nominal values the higher order terms in the Taylor series can be neglected, resulting in the following form, representing two matrix equations describing the change of the states and the correlation between states and outputs of the plant.…”

“…According to Williams and Lawrence (2007) the general nonlinear, time-varying state equation can be written as In (1), x represents the state vector of the plant, u is the control vector, y is the vector for the outputs, f and h are time-dependent nonlinear functions, t is time. From the representation displayed in (1), in this paper we develop a linearized model with simplifying as the gas turbine is considered as a time-invariable system, although in reality some deterioration (e.g.…”

Quadrotor flight stability system with Routh stability and Lyapunov analysis

“…(17) Equation (17) is the Lyapunov second method [12]. A system is said to be stable if it produces a symmetric positive definite matrix , where the matrix is a positive definite matrix shown in equation (18).…”

Parameterization and Observability Analysis of Scalable Battery Clusters for Onboard Thermal Management

“…It can guarantee fast convergence of the estimated states to those of the real plant under uncertain initial conditions, e.g. a Luenberger observer [15], or optimize the estimation by balancing the effect of process and measurement noises, e.g. a Kalman filter [16].…”